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A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

A day full of math games & activities. Find one near you.

# 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 a cubic expression.

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

Let us see how to expand (x-y)^{3}.

**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) = 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})

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

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

### Thus, the expansion of (x-y)^{3} is x^{3 }- y^{3 }- 3x^{2}y + 3xy^{2}

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