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What is the completely factored form of xy3 – x3y? (The 3's are powers if it wasn't clear.)

A. xy(y + x)(y – x)
B. xy(y – x)(y – x)
C. xy(x - y)(x^2 + xy + y^2)
D. xy(x - y)(y^2 + xy + x^2)

thanks all!

Respuesta :

sergio3007
the correct answer would be xy(y-x)(y+x)

Answer:

Option A is correct

[tex]xy(y-x)(y+x)[/tex]

Step-by-step explanation:

GCF(Greatest Common Factor) defined as the largest number that divide the two numbers

Given the equation:

[tex]xy^3-x^3y[/tex]

To find the completely factored form of the given equation.

GCF of [tex]x^3y[/tex] and [tex]xy^3[/tex] is, [tex]xy[/tex]

then;

[tex]xy \cdot y^2 - xy \cdot x^2[/tex]

Using distributive property: [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex]xy(y^2-x^2)[/tex]

Using the identity rule:

[tex](a^2-b^2) =(a-b)(a+b)[/tex]

then;

[tex]xy(y-x)(y+x)[/tex]

Therefore, the completely factored form of the given equation is, [tex]xy(y-x)(y+x)[/tex]

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