Precalculus Examples

$p (a) = a^{3} - 5$ ; Find $p (x - 4)$

Step 1

Replace the variable $a$ with $x - 4$ in the expression.

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

Step 2

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

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Step 2.1

Remove parentheses.

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

Step 2.2

Simplify each term.

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Step 2.2.1

Use the Binomial Theorem.

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

Step 2.2.2

Simplify each term.

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Step 2.2.2.1

Multiply $- 4$ by $3$ .

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

Step 2.2.2.2

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

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

Step 2.2.2.3

Multiply $16$ by $3$ .

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

Step 2.2.2.4

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

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

Step 2.3

Subtract $5$ from $- 64$ .

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