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# What is the Completely Factored Form of xy^{3} - x^{3}y?

1) xy(y + x)(y - x) 2) xy(y - x)(y - x).

**Solution:**

Factorizing a polynomial refers to writing the polynomial as a product of its factors. We will be solving the given equation to answer this question

Factored form of a polynomial can be obtained by various methods. Here, we will take out the common factors first.

Given the polynomial xy^{3} - x^{3}y

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

Now, use the algebraic identity a^{2} - b^{2} = (a - b)(a + b)

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

Hence, the completely factored form of xy^{3} - x^{3}y 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).

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