Basic Math Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to

$3 a$ .

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

Step 2.2

Raise

$3$ to the power of

$3$ .

$27 a^{3} + 3 {(3 a)}^{2} \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.3

Apply the product rule to

$3 a$ .

$27 a^{3} + 3 (3^{2} a^{2}) \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.4

Multiply

$3$ by

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

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Step 2.4.1

Move

$3^{2}$ .

$27 a^{3} + 3^{2} \cdot 3 a^{2} \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.4.2

Multiply

$3^{2}$ by

$3$ .

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Step 2.4.2.1

Raise

$3$ to the power of

$1$ .

$27 a^{3} + 3^{2} \cdot 3^{1} a^{2} \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.4.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$27 a^{3} + 3^{2 + 1} a^{2} \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.4.3

Add

$2$ and

$1$ .

$27 a^{3} + 3^{3} a^{2} \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.5

Raise

$3$ to the power of

$3$ .

$27 a^{3} + 27 a^{2} \cdot - 5 + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.6

Multiply

$- 5$ by

$27$ .

$27 a^{3} - 135 a^{2} + 3 (3 a) {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.7

Multiply

$3$ by

$3$ .

$27 a^{3} - 135 a^{2} + 9 a {(- 5)}^{2} + {(- 5)}^{3}$

Step 2.8

Raise

$- 5$ to the power of

$2$ .

$27 a^{3} - 135 a^{2} + 9 a \cdot 25 + {(- 5)}^{3}$

Step 2.9

Multiply

$25$ by

$9$ .

$27 a^{3} - 135 a^{2} + 225 a + {(- 5)}^{3}$

Step 2.10

Raise

$- 5$ to the power of

$3$ .

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