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

Axy(y + x)(y – x)
Bxy(y – x)(y – x)
Cxy(x - y)(x^2 + xy + y^2)
Dxy(x - y)(y^2 + xy + x^2)

thanks all!

Verified Answer :

sergio3007

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

Answer:

Option A is correct

\(xy(y-x)(y+x)\)

Step-by-step explanation:

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

Given the equation:

\(xy^3-x^3y\)

To find the completely factored form of the given equation.

GCF of \(x^3y\) and \(xy^3\) is, \(xy\)

then;

\(xy \cdot y^2 - xy \cdot x^2\)

Using distributive property: \(a \cdot (b+c) = a\cdot b+ a\cdot c\)

\(xy(y^2-x^2)\)

Using the identity rule:

\((a^2-b^2) =(a-b)(a+b)\)

then;

\(xy(y-x)(y+x)\)

Therefore, the completely factored form of the given equation is, \(xy(y-x)(y+x)\)

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