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]
