Precalculus Examples

$g (n) = n^{3} - 5 n^{2}$ ; Find $g (- 4 n)$

Step 1

Replace the variable $n$ with $- 4 n$ in the expression.

$g (- 4 n) = {(- 4 n)}^{3} - 5 {(- 4 n)}^{2}$

Step 2

Simplify ${(- 4 n)}^{3} - 5 {(- 4 n)}^{2}$ .

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Step 2.1

Remove parentheses.

${(- 4 n)}^{3} - 5 {(- 4 n)}^{2}$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the product rule to $- 4 n$ .

${(- 4)}^{3} n^{3} - 5 {(- 4 n)}^{2}$

Step 2.2.2

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

$- 64 n^{3} - 5 {(- 4 n)}^{2}$

Step 2.2.3

Apply the product rule to $- 4 n$ .

$- 64 n^{3} - 5 ({(- 4)}^{2} n^{2})$

Step 2.2.4

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

$- 64 n^{3} - 5 (16 n^{2})$

Step 2.2.5

Multiply $16$ by $- 5$ .

$- 64 n^{3} - 80 n^{2}$