Pre-Algebra Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $2 a$ .

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

Step 2.2

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

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

Step 2.3

Apply the product rule to $2 a$ .

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

Step 2.4

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

$8 a^{3} + 3 (4 a^{2}) \cdot 3 + 3 (2 a) \cdot 3^{2} + 3^{3}$

Step 2.5

Multiply $4$ by $3$ .

$8 a^{3} + 12 a^{2} \cdot 3 + 3 (2 a) \cdot 3^{2} + 3^{3}$

Step 2.6

Multiply $3$ by $12$ .

$8 a^{3} + 36 a^{2} + 3 (2 a) \cdot 3^{2} + 3^{3}$

Step 2.7

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 2.7.1

Move $3^{2}$ .

$8 a^{3} + 36 a^{2} + 3^{2} \cdot 3 (2 a) + 3^{3}$

Step 2.7.2

Multiply $3^{2}$ by $3$ .

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Step 2.7.2.1

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

$8 a^{3} + 36 a^{2} + 3^{2} \cdot 3^{1} (2 a) + 3^{3}$

Step 2.7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 a^{3} + 36 a^{2} + 3^{2 + 1} (2 a) + 3^{3}$

Step 2.7.3

Add $2$ and $1$ .

$8 a^{3} + 36 a^{2} + 3^{3} (2 a) + 3^{3}$

Step 2.8

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

$8 a^{3} + 36 a^{2} + 27 (2 a) + 3^{3}$

Step 2.9

Multiply $2$ by $27$ .

$8 a^{3} + 36 a^{2} + 54 a + 3^{3}$

Step 2.10

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

$8 a^{3} + 36 a^{2} + 54 a + 27$