Basic Math Examples

$8 {(a - 3 b)}^{3} - 1$

Step 1

Use the Binomial Theorem.

$8 (a^{3} + 3 a^{2} (- 3 b) + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}) - 1$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$8 (a^{3} + 3 \cdot - 3 a^{2} b + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}) - 1$

Step 2.2

Multiply $3$ by $- 3$ .

$8 (a^{3} - 9 a^{2} b + 3 a {(- 3 b)}^{2} + {(- 3 b)}^{3}) - 1$

Step 2.3

Apply the product rule to $- 3 b$ .

$8 (a^{3} - 9 a^{2} b + 3 a ({(- 3)}^{2} b^{2}) + {(- 3 b)}^{3}) - 1$

Step 2.4

Rewrite using the commutative property of multiplication.

$8 (a^{3} - 9 a^{2} b + 3 \cdot {(- 3)}^{2} a b^{2} + {(- 3 b)}^{3}) - 1$

Step 2.5

Raise $- 3$ to the power of $2$ .

$8 (a^{3} - 9 a^{2} b + 3 \cdot 9 a b^{2} + {(- 3 b)}^{3}) - 1$

Step 2.6

Multiply $3$ by $9$ .

$8 (a^{3} - 9 a^{2} b + 27 a b^{2} + {(- 3 b)}^{3}) - 1$

Step 2.7

Apply the product rule to $- 3 b$ .

$8 (a^{3} - 9 a^{2} b + 27 a b^{2} + {(- 3)}^{3} b^{3}) - 1$

Step 2.8

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

$8 (a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}) - 1$

Step 3

Apply the distributive property.

$8 a^{3} + 8 (- 9 a^{2} b) + 8 (27 a b^{2}) + 8 (- 27 b^{3}) - 1$

Step 4

Simplify.

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Step 4.1

Multiply $- 9$ by $8$ .

$8 a^{3} - 72 (a^{2} b) + 8 (27 a b^{2}) + 8 (- 27 b^{3}) - 1$

Step 4.2

Multiply $27$ by $8$ .

$8 a^{3} - 72 (a^{2} b) + 216 (a b^{2}) + 8 (- 27 b^{3}) - 1$

Step 4.3

Multiply $- 27$ by $8$ .

$8 a^{3} - 72 (a^{2} b) + 216 (a b^{2}) - 216 b^{3} - 1$

Step 5

Remove parentheses.

$8 a^{3} - 72 a^{2} b + 216 a b^{2} - 216 b^{3} - 1$