Precalculus Examples

${(2 x - 3)}^{3}$

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $2 x$ .

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

Step 2.2

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

$8 x^{3} + 3 {(2 x)}^{2} \cdot - 3 + 3 (2 x) {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.3

Apply the product rule to $2 x$ .

$8 x^{3} + 3 (2^{2} x^{2}) \cdot - 3 + 3 (2 x) {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.4

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

$8 x^{3} + 3 (4 x^{2}) \cdot - 3 + 3 (2 x) {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.5

Multiply $4$ by $3$ .

$8 x^{3} + 12 x^{2} \cdot - 3 + 3 (2 x) {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.6

Multiply $- 3$ by $12$ .

$8 x^{3} - 36 x^{2} + 3 (2 x) {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.7

Multiply $2$ by $3$ .

$8 x^{3} - 36 x^{2} + 6 x {(- 3)}^{2} + {(- 3)}^{3}$

Step 2.8

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

$8 x^{3} - 36 x^{2} + 6 x \cdot 9 + {(- 3)}^{3}$

Step 2.9

Multiply $9$ by $6$ .

$8 x^{3} - 36 x^{2} + 54 x + {(- 3)}^{3}$

Step 2.10

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

$8 x^{3} - 36 x^{2} + 54 x - 27$