Precalculus Examples

${(x - 4)}^{3} - 5$

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

$x^{3} + 3 x^{2} \cdot - 4 + 3 x {(- 4)}^{2} + {(- 4)}^{3} - 5$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $- 4$ by $3$ .

$x^{3} - 12 x^{2} + 3 x {(- 4)}^{2} + {(- 4)}^{3} - 5$

Step 1.2.2

Raise $- 4$ to the power of $2$ .

$x^{3} - 12 x^{2} + 3 x \cdot 16 + {(- 4)}^{3} - 5$

Step 1.2.3

Multiply $16$ by $3$ .

$x^{3} - 12 x^{2} + 48 x + {(- 4)}^{3} - 5$

Step 1.2.4

Raise $- 4$ to the power of $3$ .

$x^{3} - 12 x^{2} + 48 x - 64 - 5$

Step 2

Subtract $5$ from $- 64$ .

$x^{3} - 12 x^{2} + 48 x - 69$