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 $3$ .

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