Question

Which is the completely factored from of xy^3-x^3y

Answer 1

Answer:

$xy(y+x)(y-x)$

Step-by-step explanation:

To factor the expression, remove the greatest common factor or GCF from each term. Both terms share in common xy. The expression becomes:

$xy^3-x^3y\\xy(y^2-x^2)$

What remains in the parenthesis is a different of perfect squares. Factor the difference of perfect squares into two binomials of the form (x+a)(x-a) where a is the square root of $(x^2-a^2)$.

So the expression becomes:

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