Algebra Examples

{(x - y)}^{3}

${(x - y)}^{3}$

Step 1

Use the Binomial Theorem.

x^{3} + 3 x^{2} (- y) + 3 x {(- y)}^{2} + {(- y)}^{3}

$x^{3} + 3 x^{2} (- y) + 3 x {(- y)}^{2} + {(- y)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

x^{3} + 3 \cdot - 1 x^{2} y + 3 x {(- y)}^{2} + {(- y)}^{3}

$x^{3} + 3 \cdot - 1 x^{2} y + 3 x {(- y)}^{2} + {(- y)}^{3}$

Step 2.2

Multiply

3

$3$ by

- 1

$- 1$ .

x^{3} - 3 x^{2} y + 3 x {(- y)}^{2} + {(- y)}^{3}

$x^{3} - 3 x^{2} y + 3 x {(- y)}^{2} + {(- y)}^{3}$

Step 2.3

Apply the product rule to

- y

$- y$ .

x^{3} - 3 x^{2} y + 3 x ({(- 1)}^{2} y^{2}) + {(- y)}^{3}

$x^{3} - 3 x^{2} y + 3 x ({(- 1)}^{2} y^{2}) + {(- y)}^{3}$

Step 2.4

Rewrite using the commutative property of multiplication.

x^{3} - 3 x^{2} y + 3 \cdot {(- 1)}^{2} x y^{2} + {(- y)}^{3}

$x^{3} - 3 x^{2} y + 3 \cdot {(- 1)}^{2} x y^{2} + {(- y)}^{3}$

Step 2.5

Raise

- 1

$- 1$ to the power of

2

$2$ .

x^{3} - 3 x^{2} y + 3 \cdot 1 x y^{2} + {(- y)}^{3}

$x^{3} - 3 x^{2} y + 3 \cdot 1 x y^{2} + {(- y)}^{3}$

Step 2.6

Multiply

3

$3$ by

1

$1$ .

x^{3} - 3 x^{2} y + 3 x y^{2} + {(- y)}^{3}

$x^{3} - 3 x^{2} y + 3 x y^{2} + {(- y)}^{3}$

Step 2.7

Apply the product rule to

- y

$- y$ .

x^{3} - 3 x^{2} y + 3 x y^{2} + {(- 1)}^{3} y^{3}

$x^{3} - 3 x^{2} y + 3 x y^{2} + {(- 1)}^{3} y^{3}$

Step 2.8

Raise

- 1

$- 1$ to the power of

3

$3$ .

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

$x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$

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

$x^{3} - 3 x^{2} y + 3 x y^{2} - y^{3}$

{(x - y)}^{3}

${(x - y)}^{3}$

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