Expand the Trigonometric Expression (5a-1)^3

${(5 a - 1)}^{3}$

Step 1

Use the Binomial Theorem.

${(5 a)}^{3} + 3 {(5 a)}^{2} \cdot - 1 + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

Step 2

Simplify each term.

Apply the product rule to $5 a$ .

$5^{3} a^{3} + 3 {(5 a)}^{2} \cdot - 1 + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

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

$125 a^{3} + 3 {(5 a)}^{2} \cdot - 1 + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

Apply the product rule to $5 a$ .

$125 a^{3} + 3 (5^{2} a^{2}) \cdot - 1 + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

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

$125 a^{3} + 3 (25 a^{2}) \cdot - 1 + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

Multiply $25$ by $3$ .

$125 a^{3} + 75 a^{2} \cdot - 1 + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

Multiply $- 1$ by $75$ .

$125 a^{3} - 75 a^{2} + 3 (5 a) {(- 1)}^{2} + {(- 1)}^{3}$

Multiply $5$ by $3$ .

$125 a^{3} - 75 a^{2} + 15 a {(- 1)}^{2} + {(- 1)}^{3}$

Raise $- 1$ to the power of $2$ .

$125 a^{3} - 75 a^{2} + 15 a \cdot 1 + {(- 1)}^{3}$

Multiply $15$ by $1$ .

$125 a^{3} - 75 a^{2} + 15 a + {(- 1)}^{3}$

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

$125 a^{3} - 75 a^{2} + 15 a - 1$