Question

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!

Answer 1

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

Answer 2

Option A is correct

`xy(y-x)(y+x)`

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)`