Precalculus Examples

${(x - 3)}^{3} - 4$

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $- 3$ by $3$ .

$x^{3} - 9 x^{2} + 3 x {(- 3)}^{2} + {(- 3)}^{3} - 4$

Step 1.2.2

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

$x^{3} - 9 x^{2} + 3 x \cdot 9 + {(- 3)}^{3} - 4$

Step 1.2.3

Multiply $9$ by $3$ .

$x^{3} - 9 x^{2} + 27 x + {(- 3)}^{3} - 4$

Step 1.2.4

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

$x^{3} - 9 x^{2} + 27 x - 27 - 4$

Step 2

Subtract $4$ from $- 27$ .

$x^{3} - 9 x^{2} + 27 x - 31$