Basic Math Examples

{(a - 3 b)}^{3}

${(a - 3 b)}^{3}$

Step 1

Use the Binomial Theorem.

a^{3} + 3 a^{2} (- 3 b) + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}

$a^{3} + 3 a^{2} (- 3 b) + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

a^{3} + 3 \cdot - 3 a^{2} b + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}

$a^{3} + 3 \cdot - 3 a^{2} b + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}$

Step 2.2

Multiply

3

$3$ by

- 3

$- 3$ .

a^{3} - 9 a^{2} b + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}

$a^{3} - 9 a^{2} b + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}$

Step 2.3

Apply the product rule to

- 3 b

$- 3 b$ .

a^{3} - 9 a^{2} b + 3 a ({(- 3)}^{2} b^{2}) + {(- 3 b)}^{3}

$a^{3} - 9 a^{2} b + 3 a ({(- 3)}^{2} b^{2}) + {(- 3 b)}^{3}$

Step 2.4

Rewrite using the commutative property of multiplication.

a^{3} - 9 a^{2} b + 3 \cdot {(- 3)}^{2} a b^{2} + {(- 3 b)}^{3}

$a^{3} - 9 a^{2} b + 3 \cdot {(- 3)}^{2} a b^{2} + {(- 3 b)}^{3}$

Step 2.5

Raise

- 3

$- 3$ to the power of

2

$2$ .

a^{3} - 9 a^{2} b + 3 \cdot 9 a b^{2} + {(- 3 b)}^{3}

$a^{3} - 9 a^{2} b + 3 \cdot 9 a b^{2} + {(- 3 b)}^{3}$

Step 2.6

Multiply

3

$3$ by

9

$9$ .

a^{3} - 9 a^{2} b + 27 a b^{2} + {(- 3 b)}^{3}

$a^{3} - 9 a^{2} b + 27 a b^{2} + {(- 3 b)}^{3}$

Step 2.7

Apply the product rule to

- 3 b

$- 3 b$ .

a^{3} - 9 a^{2} b + 27 a b^{2} + {(- 3)}^{3} b^{3}

$a^{3} - 9 a^{2} b + 27 a b^{2} + {(- 3)}^{3} b^{3}$

Step 2.8

Raise

- 3

$- 3$ to the power of

3

$3$ .

a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}

$a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}$

a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}

$a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}$