What is the completely factored form of xy³ - x³y?

Solution:

Given a polynomial xy³ - x³y.

Factoring polynomials can be done using different methods. 

Let us use the method of taking out the common factors

Given: xy³ - x³y

xy³ - x³y = xy(y² - x²)

From the algebraic identity,

a² - b² = (a + b)(a - b)

So the given polynomial can be written as

xy(y² - x²) = xy(y + x)(y - x)

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

What is the completely factored form of xy³ - x³y?

Summary:

The completely factored form of xy³ - x³y is xy(y + x)(y - x).