Basic Math Examples

{(u - v)}^{3}

${(u - v)}^{3}$

Step 1

Use the Binomial Theorem.

u^{3} + 3 u^{2} (- v) + 3 u {(- v)}^{2} + {(- v)}^{3}

$u^{3} + 3 u^{2} (- v) + 3 u {(- v)}^{2} + {(- v)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

u^{3} + 3 \cdot - 1 u^{2} v + 3 u {(- v)}^{2} + {(- v)}^{3}

$u^{3} + 3 \cdot - 1 u^{2} v + 3 u {(- v)}^{2} + {(- v)}^{3}$

Step 2.2

Multiply

3

$3$ by

- 1

$- 1$ .

u^{3} - 3 u^{2} v + 3 u {(- v)}^{2} + {(- v)}^{3}

$u^{3} - 3 u^{2} v + 3 u {(- v)}^{2} + {(- v)}^{3}$

Step 2.3

Apply the product rule to

- v

$- v$ .

u^{3} - 3 u^{2} v + 3 u ({(- 1)}^{2} v^{2}) + {(- v)}^{3}

$u^{3} - 3 u^{2} v + 3 u ({(- 1)}^{2} v^{2}) + {(- v)}^{3}$

Step 2.4

Rewrite using the commutative property of multiplication.

u^{3} - 3 u^{2} v + 3 \cdot {(- 1)}^{2} u v^{2} + {(- v)}^{3}

$u^{3} - 3 u^{2} v + 3 \cdot {(- 1)}^{2} u v^{2} + {(- v)}^{3}$

Step 2.5

Raise

- 1

$- 1$ to the power of

2

$2$ .

u^{3} - 3 u^{2} v + 3 \cdot 1 u v^{2} + {(- v)}^{3}

$u^{3} - 3 u^{2} v + 3 \cdot 1 u v^{2} + {(- v)}^{3}$

Step 2.6

Multiply

3

$3$ by

1

$1$ .

u^{3} - 3 u^{2} v + 3 u v^{2} + {(- v)}^{3}

$u^{3} - 3 u^{2} v + 3 u v^{2} + {(- v)}^{3}$

Step 2.7

Apply the product rule to

- v

$- v$ .

u^{3} - 3 u^{2} v + 3 u v^{2} + {(- 1)}^{3} v^{3}

$u^{3} - 3 u^{2} v + 3 u v^{2} + {(- 1)}^{3} v^{3}$

Step 2.8

Raise

- 1

$- 1$ to the power of

3

$3$ .

u^{3} - 3 u^{2} v + 3 u v^{2} - v^{3}

$u^{3} - 3 u^{2} v + 3 u v^{2} - v^{3}$

u^{3} - 3 u^{2} v + 3 u v^{2} - v^{3}

$u^{3} - 3 u^{2} v + 3 u v^{2} - v^{3}$