Expand the Trigonometric Expression (5a+2)^3

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

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.

Apply the product rule to $5 a$ .

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

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

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

Apply the product rule to $5 a$ .

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

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

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

Multiply $25$ by $3$ .

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

Multiply $2$ by $75$ .

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

Multiply $5$ by $3$ .

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

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

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

Multiply $4$ by $15$ .

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

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

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