# Expand (x-y)^{3}

Algebraic identities are equations where the value of the left-hand side of the equation is identically equal to the value of the right-hand side of the equation. The expression (x-y)^{3} is an cubic expression.

## Answer: The expansion of (x-y)^{3} is x^{3}-y^{3}-3x^{2}y+3xy^{2}

Let us see, how to solve.

## Explanation:

The expression (x-y)^{3} can be written as, (x-y)(x-y)(x-y)

First simplify (x-y)(x-y) by binomial multiplication.

(x-y)(x-y) = xx - xy - yx + yy

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

Now multiply (x-y) with x^{2} - 2xy + y^{2}

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

= xx^{2} - 2xyx + xy^{2} - yx^{2} + 2xyy - y^{3}

= x^{3} - 2x^{2}y + xy^{2} - yx^{2} + 2xy^{2} - y^{3}

= x^{3} - 3x^{2}y + 3xy^{2} - y^{3}