# What is the completely factored form of xy^{3} - x^{3}y?

**Solution:**

Given a polynomial xy^{3} - x^{3}y.

Factoring polynomials can be done using different methods.

Let us use the method of taking out the common factors

Given: xy^{3} - x^{3}y

xy^{3} - x^{3}y = xy(y^{2} - x^{2})

From the algebraic identity,

a^{2} - b^{2} = (a + b)(a - b)

So the given polynomial can be written as

xy(y^{2} - x^{2}) = xy(y + x)(y - x)

Therefore, the completely factored form is xy(y + x)(y - x).

## What is the completely factored form of xy^{3} - x^{3}y?

**Summary:**

The completely factored form of xy^{3} - x^{3}y is xy(y + x)(y - x).