A Graphical Approach to Algebra & Trigonometry (7th Edition)

Chapter 10

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; Since the natural number which are less than 8 ... more

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; Since the integers which lies between 4 and 10 ... more

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; There are four seasons which are Summer, Autumn... more

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; There are total 12 months in a year which are ... more

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; Since there is no women who is the president of... more

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; Since there is no living human whose age is ... more

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; Since the alphabet which lies between K and M ... more

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; Since the alphabet which lies between D and H ... more

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; Since the positive even integers are 2, 4, 6, 8... more

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; Since the multiples of 5 are 5, 10, 15, 20, 25... more

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Set of all the positive even integers and set of ... more

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Set of all the natural numbers less than 8, set of... more

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The statement represent that 5 is a element of the... more

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The statement represent that 6 is an element of ... more

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The statement represent that 2 is an element of ... more

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The statement represent that 1 is an element of ... more

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The statement represent that 7 is not an element ... more

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The statement represent that 7 is not an element ... more

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Since each and every element of both the sets are ... more

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Since the set does not contain 0 but the set ... more

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All the elements of the set are also present in ... more

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In this case, but that means all the elements of... more

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An empty set is a subset of each set except itself... more

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Both the elements of the set are also present in ... more

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All the elements of the set are also present in ... more

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All the elements of the set are not present in ... more

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In this case, but also but that means each ... more

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All the elements of the set are also present in ... more

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Here the set does not contain each element of the... more

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All the elements of the set are also present in ... more

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Both the elements of the set are also present in ... more

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Both the elements of the set are also present in ... more

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Let, and Since each element of the set are also ... more

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Let,  and   Since the element of the set is also ... more

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The intersection of set and is the set of ... more

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The intersection of set and is the set of ... more

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The intersection of set and is the set of ... more

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The intersection of set and is the set of ... more

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The intersection of set and is the set of ... more

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The union of sets and is the set of elements ... more

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The union of sets and is the set of elements ... more

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The union of sets and is the set of elements ... more

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The union of sets and is the set of elements ... more

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The union of sets and is the set of elements ... more

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; The set is called a complement of the set and... more

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; The set is called a complement of the set and... more

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; The set is called a complement of the set and... more

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; The set is called a complement of the set and... more

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  ; The intersection of set and is the set of ... more

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  ; The intersection of set and is the set of ... more

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  ; The intersection of set and is the set of ... more

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  ; The intersection of set and is the set of ... more

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  ; The intersection of set and is the set of ... more

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; The union of sets and is the set of elements ... more

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; The union of sets and is the set of elements ... more

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; The union of sets and is the set of elements ... more

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; The union of sets and is the set of elements ... more

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; The union of sets and is the set of elements ... more

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; The intersection of any two sets and is the ... more

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; The union of any two sets and is the set of ... more

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; Apply product rule, when base of product of all... more

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; Apply product rule, when base of product all ... more

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1 ; Apply zero exponent property, when exponent is... more

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-1 ; Apply zero exponent property, when exponent ... more

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1 ; Apply zero exponent property, when exponent is... more

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1 ; Apply zero exponent property, when exponent is... more

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; Apply power rule, when base has two exponents ... more

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; Apply power rule, when base has two exponents ... more

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; Apply power rule, when base has two exponents ... more

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; Apply power rule, when base has two exponents ... more

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; Apply power rule, when base has two exponents ... more

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; Apply power rule, when base has two exponents ... more

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; Trinomial is the equation of three terms. ... more

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; Add the coefficients of like terms. and has ... more

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; Add the coefficients of like terms. and has ... more

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; Subtract the coefficients of like terms. and ... more

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; Subtract the coefficients of like terms. and ... more

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; First subtract the coefficients of like terms ... more

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; First subtract the coefficients of like terms ... more

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; Apply FOIL method, multiply the first term of ... more

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; Apply FOIL method, multiply the first term of ... more

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; Apply FOIL method, multiply the first term of ... more

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; Apply FOIL method, multiply the first term of ... more

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; Using distributive property, multiply monomial... more

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; Using distributive property, multiply monomial... more

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; Apply FOIL method, multiply first term of first... more

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; Apply FOIL method, multiply first term of first... more

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; Apply FOIL method, multiply first term of first... more

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; Use formula of product of sum and difference of... more

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; Use formula of product of sum and difference of... more

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; Use formula of square of binomial, square of ... more

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; Use formula of square of binomial, square of ... more

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; Use formula of square of binomial, square of ... more

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; Use formula of square of binomial, square of ... more

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; Use formula of square of binomial, square of ... more

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; Using property, .Let a=4y-1, b=z.  ; more

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; Using formula , Here a=3q+5, b=p.Using formula... more

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; Using formula ,Here a=(9r-s), b=2. Using ... more

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; Using the formula .Here x=(3a+b), y=1. ; more

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; Using formula and Here x=(2m+7), y=n.  ; more

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; Simplifying the product, ; more

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; Simplifying the product, ; more

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; Subtracting the coefficients of like terms, ; more

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; Using the formula . ; more

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; Using the formula . ; more

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; Adding the coefficients of like term,  ; more

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; Simplifying the product, ; more

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; Using formula Here a=7m, b=2n. ; more

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; Using formula .Here a=3p, b=5. ; more

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; Simplifying the product,Adding the like ... more

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; Simplifying the product, ; more

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; Simplifying the product, ; more

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; Simplifying the product, ; more

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; Simplifying the product, ; more

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Using the identity . ; Using the identity . ; ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the greatest common factor first ... more

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; For finding the factor, first group the terms ... more

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; For finding the factor, first group the terms ... more

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; For finding the factor, first group the terms ... more

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; For finding the factor, first group the terms ... more

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; For finding the factor, first group the terms ... more

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; For finding the factor, first group the terms ... more

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; Since =8 is positive, so as a factor possible ... more

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; Since =6 is positive, so as a factor possible ... more

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; Consider,Since =9 is positive, so as a factor ... more

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; Consider,Since =1 is positive, so as a factor ... more

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; Since =14 is positive, so as a factor possible ... more

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; Since =6 is positive, so as a factor possible ... more

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; Since =12 is positive, so as a factor possible ... more

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; Since =5 is positive, so as a factor possible ... more

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; Since =30 is positive, so as a factor possible ... more

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; Consider,Now,Since =1 is positive, so as a ... more

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; Consider,Since =18 is positive, so as a factor ... more

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; Consider,Since =24 is positive, so as a factor ... more

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; For finding the factor, it is known that and... more

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; \begin{aligned} 20p^{2}-100 pq+125q^{2}&=5\cdot... more

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; For finding the factor, First take the common ... more

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; For finding the factor, it is known that and... more

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; For finding the factor, it is known that and... more

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; For finding the factor, it is known that . Now ... more

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; For finding the factor, it is known that . Now ... more

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; \begin{aligned} (5r+2s)^{2}+6(5r+2s)+9&=(5r+2s... more

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Yes. ; Since  ; more

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; For finding the factor, it is known that and... more

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  ; Write as a difference of squares, that is, ... more

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; Write as a difference of squares, that is,... more

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; Write as a difference of squares, that is, ... more

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; Write as a difference of squares, that is, ... more

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; Write as a difference of squares, that is, ... more

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; Write as a difference of squares, that is, ... more

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; Write as a difference of squares, that is, ... more

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Factor by using the difference of squares formula... more

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Rewrite by using the formula,   So, Therefore ... more

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; First factor out from .Then write as a ... more

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; Write as a sum of cubes, that is, rewrite 27 ... more

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; Write as a difference of cubes, that is, ... more

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; Write as a difference of cubes, that is, ... more

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; Write as a sum of cubes, that is, rewrite as... more

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; First factor out from .Then write as a sum of... more

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. ; Write as a difference of cubes, that is, ... more

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; Write as a difference of cubes, that is, ... more

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; First factor out from .Then write as a ... more

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The factorisation is incorrect because in the ... more

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; To factor the given polynomial, write as in ... more

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. ; To factor the given polynomial, write as in ... more

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; To factor the given expression, substitute ... more

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; To factor the given expression, substitute ... more

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; To factor the given expression, substitute ... more

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; To factor the given expression, substitute ... more

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; Consider the trinomial . Now write as and use... more

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; Since the greatest common factor is , so use ... more

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; Group the terms of the given expression in such... more

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; To factor the given expression, substitute ... more

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; Since the greatest common factor is , so use ... more

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; Write as , and then factor the trinomial ... more

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; Write as , as and 49 as . And then use the ... more

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; Write as , as and 25 as . And then use the ... more

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; Write as and as . And then use the formula ... more

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; To factor the given polynomial, write as in ... more

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; Write as and 216 as . And then use the ... more

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; Write as and 16 as , then use the formula, ... more

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; Write as , and group the terms which have ... more

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; Write as and 9 as , then use the formula, to... more

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; Write as , and group the terms which have ... more

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; Write the expression as a sum of cubes as ... more

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Factor does not exist ; Write the expression as a ... more

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; Write the expression as a difference of squares... more

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; Substitute as in the expression and simplify as... more

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; Substitute as in the expression and simplify as... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; Domain for a rational expression of form where ... more

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; First factor the rational expression as stated ... more

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; First factor the rational expression as stated ... more

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; Take out 8 and 9 as a common from numerator ... more

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; Take out 10 and 15 as a common from numerator ... more

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; Using the fundamental principle of fractions ... more

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; Using the fundamental principle of fractions ... more

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; Take out as a common from the numerator term of... more

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; Take out as a common from the numerator term of... more

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; First, factor the numerator term of the ... more

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; First, factor the numerator term of the ... more

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; First, factor the numerator term of the ... more

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; First, factor the numerator term of the ... more

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; Apply the property of dividing fractions if is ... more

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; Apply the property of dividing fractions if is ... more

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; Apply the property of dividing fractions if is ... more

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1 ; Apply the property of multiplying fractions if... more

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; Apply the property of multiplying fractions if ... more

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; Apply the property of multiplying fractions if ... more

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; Apply the property of dividing fractions if is ... more

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; Apply the property of multiplying fractions if ... more

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1 ; First, factor the expression using the middle ... more

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; First, factor the expression using the middle ... more

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; Apply the property of dividing fractions if is ... more

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; Apply the property of dividing fractions if is ... more

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; Apply the property of dividing fractions if is ... more

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; First, factor the expression using the middle ... more

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; First, factor the expression using the identity... more

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; Given, First, factor the expression using the ... more

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; Given, First, factor the expression using the ... more

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; Given, First, factor the expression using the ... more

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The expressions can not be simplified further ... more

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To find the least common denominator, first, find ... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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1 ; Given that, Since the denominators of both the... more

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2.4 ; Given that, Since the denominators of both ... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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; Given that, The Least Common Denominator is .... more

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; Given that, .Rewrite both the given expressions... more

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; The expression is . Rewrite both the terms so ... more

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; Given that, .Rewrite both the given expressions... more

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; Given that, .Rewrite both the given expressions... more

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;  The expression is firstly rewritten then ... more

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; All denominator are factorize by using for  ... more

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; The denominator of both term is factorize  by ... more

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; The denominator of expression is factorize by ... more

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; The denominator of expression is factorize by ... more

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; The denominator of expression is factorize by ... more

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; The denominator of expression is factorize by ... more

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; The numerator and denominator is multiplied by... more

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; The Lowest common factor of  numerator and ... more

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; To simplify it multiply it the numerator and ... more

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;  Multiply the numerator and denominator by ... more

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; Multiply the  numerator and denominator by  ... more

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; The lowest common denominator is 2 therefore ... more

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; The lowest common denominator is  hence  ... more

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; The lowest common denominator of all fraction ... more

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The expression can be simplified by using the ... more

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; To simplify use  the exponent formula ; more

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; To simplify use  the exponent formula   ; more

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8 ; To simplify use  the exponent formula   ; more

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; To simplify use  the exponent formula ; more

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5 ; To simplify use  the exponent formula ; more

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4 ; To simplify use  the exponent formula   ; more

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-27 ; To simplify use  the exponent formula... more

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; To simplify use  the exponent formula and ; more

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;  To simplify use  the exponent formula and... more

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; To simplify use  the exponent formula and... more

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; To simplify use  the exponent formula and... more

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; To simplify use  the exponent formula   ; more

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; To simplify use  the exponent formula... more

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; To simplify use  the exponent formula  and... more

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; To simplify use  the exponent formula and... more

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; Firstly apply  the exponent formula .Then use ... more

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; To simplify use  the exponent formula   and... more

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; To simplify use  the exponent formula  and... more

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; To simplify use  the exponent formula   and... more

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1 ; To simplify use  the exponent formula   and... more

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; To simplify use  the exponent formula   and... more

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; To simplify use  the exponent formula    ; more

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; To simplify use  the exponent formula    ; more

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; To simplify use  the exponent formula   ; more

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; To simplify use  the exponent formula   and... more

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;  To simplify use  the exponent formula   and... more

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; Rearrange a and b in equation andapply the ... more

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; Apply product and quotient rule to solve the ... more

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; Simplifying the given expression using the ... more

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; Simplifying the given expression using the ... more

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; Simplifying the given expression using the ... more

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; Simplifying the given expression using the ... more

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; As the given expression is a product of sum ... more

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; As the given expression is a product of sum ... more

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; As the given expression is a special product ... more

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; As the given expression is a product of sum ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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; Factoring the given expression using the ... more

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Simplifying the given expression to write in the ... more

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; Radical notation for a expression is written ... more

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; Radical notation for a expression is written ... more

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; Radical notation for a expression is written ... more

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; For any real number , , where are positive ... more

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; For any positive real number ,, where are ... more

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; For any real number , , where are positive ... more

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; For a real number ,, where are positive ... more

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; For any real number ,, where are real numbers.... more

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If both and are positive then, the given ... more

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The statement is always true when is odd. ; The ... more

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The values of are zero or any positive numbers... more

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The given expression is the simplest form, which ... more

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5 ; 125 can be written as . So, simplify the cube ... more

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3 ; Simplify the given expression to get the final... more

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-5 ; Find the factors of -3125 and simplify the ... more

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7 ; Find the factors of 343 and simplify to get ... more

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; Find the factors of 50 and simplify to get the ... more

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; Find the factors of 45 and simplify to get the ... more

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; Find the factors of 81 and simplify to get the ... more

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; Find the factors of 250 and simplify to get the... more

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; Find the factors of 32 and simplify to get the ... more

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; Find the factors of 243 and simplify to get the... more

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; Find the factors of the expression and simplify... more

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The given radical expression is in the simplest ... more

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The given radical expression is in the simplest ... more

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The given radical expression is in the simplest ... more

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; The given radical can be expressed as, ; more

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; The given radical expression can be simplified ... more

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; The given radical expression can be simplified ... more

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; The given radical expression can be simplified ... more

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; The given radical expression can be simplified ... more

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; The given radical expression can be simplified ... more

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; The given radical expression can be simplified ... more

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; The given radical expression can be simplifies ... more

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The given radical expression cannot be simplified ... more

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The given radical expression cannot be simplified ... more

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The given radical expression cannot be simplified ... more

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The given radical expression cannot be further ... more

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; The given radical expression can be simplified ... more

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; The radical expression can be simplified as ... more

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; The given radical expression can be simplified ... more

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; The  radical expression can be simplified as ... more

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; The given radical expression can be simplified ... more

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; Using the power rule of the exponential ... more

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; Using the rules of exponents, ; more

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; Using the rules of exponents, ; more

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2\sqrt[4]{x^{3}y^{3}} ; Using the rules of ... more

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; Using the rules of exponents, ; more

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; Expression of the form can be solved using ... more

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; For the given expression, we can observe the ... more

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; For the expression of the form below, we have ... more

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; We have the formula,Applying the above formula ... more

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; We wil use the below formula for the given ... more

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; Let us open the brackets for the two ... more

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; Rationalizing the denomnator means turning the ... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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; Rationalizing the denominator means turning the... more

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Set of even natural numbers between and is given... more

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; The union of two set and is the set of all ... more

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; The intersection of two set and is the set of... more

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; Here, given sets are ,  Now, ; more

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; Simplifying the given expression using the ... more

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; Simplifying the given expression by using the ... more

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; For any nonzero real number . Using this ... more

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; Simplifying the given expression by using the ... more

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; Simplifying the given expression by using the ... more

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; Simplifying the given expression by using the ... more

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; Performing the indicated operations to simplify... more

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; As the given expression is a special product ... more

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; Performing the indicated operations to simplify... more

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; As the given expression is a product of sum ... more

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; As the given expression is a special product ... more

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; Performing the indicated operations to simplify... more

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; Factoring the given expression completely. by ... more

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; and 16 can be written as and respectively.To... more

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; Given trinomial can be written in the form of... more

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; First, do grouping the terms, and then factor ... more

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; ; 16 and can be written as and respectively. ... more

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; ; First, factorize the denominator and then ... more

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; ; First, factorize the numerator and the ... more

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; . ; and 125 can be written as and ... more

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; Factorize the all polynomial expressions. ; ... more

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; First factorize both the denominators. ; The ... more

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; Take out -1 common factor from . ; Now add both... more

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; Multiply both the numerator and denominator by... more

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; Use the exponent rule . ; more

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; Use the exponent rule .16 can be written as... more

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; Use the exponent rule .64 and 27 can be written... more

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; Use the exponent rule .8 and 27 can be written ... more

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; First apply the exponent rule . ; Now, apply ... more

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; First apply the exponent rule . Now, apply the ... more

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; First apply the exponent rule and then . ; Now... more

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; First apply the exponent rule and then . ; Now... more

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2 ; Use .16 can be written as . ; Now, apply the ... more

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; Multiply and divide by to remove the radical ... more

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; The term under root can be simplified by prime ... more

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; Multiply and divide by to remove the radical ... more

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; The term under root can be simplified by prime ... more

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; Multiply the by the terms in second bracket ... more

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; Multiply the terms in second bracket by and .... more

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; Multiply and divide by to remove the radical ... more

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