Algebra Examples

${(5 a + 2)}^{3}$

Step 1

Use the Binomial Theorem.

${(5 a)}^{3} + 3 {(5 a)}^{2} \cdot 2 + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $5 a$ .

$5^{3} a^{3} + 3 {(5 a)}^{2} \cdot 2 + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2.2

Raise $5$ to the power of $3$ .

$125 a^{3} + 3 {(5 a)}^{2} \cdot 2 + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2.3

Apply the product rule to $5 a$ .

$125 a^{3} + 3 (5^{2} a^{2}) \cdot 2 + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2.4

Raise $5$ to the power of $2$ .

$125 a^{3} + 3 (25 a^{2}) \cdot 2 + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2.5

Multiply $25$ by $3$ .

$125 a^{3} + 75 a^{2} \cdot 2 + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2.6

Multiply $2$ by $75$ .

$125 a^{3} + 150 a^{2} + 3 (5 a) \cdot 2^{2} + 2^{3}$

Step 2.7

Multiply $5$ by $3$ .

$125 a^{3} + 150 a^{2} + 15 a \cdot 2^{2} + 2^{3}$

Step 2.8

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

$125 a^{3} + 150 a^{2} + 15 a \cdot 4 + 2^{3}$

Step 2.9

Multiply $4$ by $15$ .

$125 a^{3} + 150 a^{2} + 60 a + 2^{3}$

Step 2.10

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

$125 a^{3} + 150 a^{2} + 60 a + 8$