Simplify (5a-3)^3 - Math help

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

Use the Binomial Theorem.

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

Simplify each term.

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Apply the product rule to $5 a$ .

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

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

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

Apply the product rule to $5 a$ .

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

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

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

Multiply $25$ by $3$ .

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

Multiply $- 3$ by $75$ .

$125 a^{3} - 225 a^{2} + 3 (5 a) {(- 3)}^{2} + {(- 3)}^{3}$

Multiply $5$ by $3$ .

$125 a^{3} - 225 a^{2} + 15 a {(- 3)}^{2} + {(- 3)}^{3}$

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

$125 a^{3} - 225 a^{2} + 15 a \cdot 9 + {(- 3)}^{3}$

Multiply $9$ by $15$ .

$125 a^{3} - 225 a^{2} + 135 a + {(- 3)}^{3}$

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

$125 a^{3} - 225 a^{2} + 135 a - 27$

Simplify (5a-3)^3

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