Basic Math Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

Multiply $3$ by $- 1$ .

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

Step 2.3

Apply the product rule to $- v$ .

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

Step 2.4

Rewrite using the commutative property of multiplication.

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

Step 2.5

Raise $- 1$ to the power of $2$ .

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

Step 2.6

Multiply $3$ by $1$ .

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

Step 2.7

Apply the product rule to $- v$ .

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

Step 2.8

Raise $- 1$ to the power of $3$ .

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