Precalculus Examples

$g (n) = - 2 n + 5$ $f (n) = - 2 n$ Find $(g \cdot f) (n)$

Step 1

Evaluate $g \cdot f$ .

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Step 1.1

Replace the function designators in $g \cdot f$ with the actual functions.

$(- 2 n + 5) \cdot (- 2 n)$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$- 2 n (- 2 n) + 5 (- 2 n)$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 2 n \cdot n + 5 (- 2 n)$

Step 1.2.2.2

Multiply $- 2$ by $5$ .

$- 2 \cdot - 2 n \cdot n - 10 n$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $n$ by $n$ by adding the exponents.

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Step 1.3.1.1

Move $n$ .

$- 2 \cdot - 2 (n \cdot n) - 10 n$

Step 1.3.1.2

Multiply $n$ by $n$ .

$- 2 \cdot - 2 n^{2} - 10 n$

Step 1.3.2

Multiply $- 2$ by $- 2$ .

$4 n^{2} - 10 n$

Step 2

Evaluate $g \cdot f$ at $n$ .

$4 {(n)}^{2} - 10 n$

Step 3

Simplify $4 {(n)}^{2} - 10 n$ .

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Step 3.1

Remove parentheses.

$4 {(n)}^{2} - 10 n$

Step 3.2

Remove parentheses.

$4 n^{2} - 10 n$