We want to factor the following expression: 25x^2−36y^8 We can factor the expression as (U+V)(U-V) where U and V are either constant integ

Question

We want to factor the following expression: 25x^2−36y^8 We can factor the expression as (U+V)(U-V) where U and V are either constant integers or single-variable expressions. What are U and V?

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Lyla 3 weeks 2021-11-08T23:17:35+00:00 2 Answers 0 views 0

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    0
    2021-11-08T23:19:04+00:00

    Answer: U= 5x*3 and V=3

    Factored: (5x^3 -3)^2

    0
    2021-11-08T23:19:17+00:00

    Answer:

    U=5\,x

    V=6\,y^4

    Step-by-step explanation:

    Recall that an expression that can be factored as (U+V)(U-V) using distributive property for multiplication of binomials, should render:  U^2-V^2 (the factorization given above is that of a difference of squares. Then, the idea is to write the original expression :

    25\,x^2-36\,y^8

    as a difference of perfect squares. Let’s examine each term and its numerical and variable form to find if they can be written as perfect squares:

    a) the term   25\,x^2=5^2\,x^2=(5x)^2 therefore, if we assign the letter U to 5\,x, the first term becomes:

    25\,x^2=(5\,x)^2=U^2

    b) the term   -36\,y^8=-6^2\,(y^4)^2=-(6\,y^4)^2  therefore, if we assign the letter V to  6\,y^4 , this second term becomes:

    -36\,y^8=-(6\,y^4)^2=-V^2

    With the above identification, our expression can now be factored as a difference of squares:

    25\,x^2-36\,y^8=(5\,x)^2-(6\,y^4)^2=U^2-V^2=(U+V)(U-V)

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