Basic Math Examples

${(15 b + 9)}^{3}$

Step 1

Use the Binomial Theorem.

${(15 b)}^{3} + 3 {(15 b)}^{2} \cdot 9 + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $15 b$ .

$15^{3} b^{3} + 3 {(15 b)}^{2} \cdot 9 + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2.2

Raise $15$ to the power of $3$ .

$3375 b^{3} + 3 {(15 b)}^{2} \cdot 9 + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2.3

Apply the product rule to $15 b$ .

$3375 b^{3} + 3 (15^{2} b^{2}) \cdot 9 + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2.4

Raise $15$ to the power of $2$ .

$3375 b^{3} + 3 (225 b^{2}) \cdot 9 + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2.5

Multiply $225$ by $3$ .

$3375 b^{3} + 675 b^{2} \cdot 9 + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2.6

Multiply $9$ by $675$ .

$3375 b^{3} + 6075 b^{2} + 3 (15 b) \cdot 9^{2} + 9^{3}$

Step 2.7

Multiply $15$ by $3$ .

$3375 b^{3} + 6075 b^{2} + 45 b \cdot 9^{2} + 9^{3}$

Step 2.8

Raise $9$ to the power of $2$ .

$3375 b^{3} + 6075 b^{2} + 45 b \cdot 81 + 9^{3}$

Step 2.9

Multiply $81$ by $45$ .

$3375 b^{3} + 6075 b^{2} + 3645 b + 9^{3}$

Step 2.10

Raise $9$ to the power of $3$ .

$3375 b^{3} + 6075 b^{2} + 3645 b + 729$