Precalculus Examples

$g (n) = 3 n - 2$ $h (n) = 3 n + 3$ Find $(2 g + 5 h) (n)$

Step 1

Replace the function designators in $(2 g + 5 h) (n)$ with the actual functions.

$(2 (3 n - 2) + 5 (3 n + 3)) (n)$

Step 2

Simplify $(2 (3 n - 2) + 5 (3 n + 3)) (n)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$(2 (3 n) + 2 \cdot - 2 + 5 (3 n + 3)) n$

Step 2.1.2

Multiply $3$ by $2$ .

$(6 n + 2 \cdot - 2 + 5 (3 n + 3)) n$

Step 2.1.3

Multiply $2$ by $- 2$ .

$(6 n - 4 + 5 (3 n + 3)) n$

Step 2.1.4

Apply the distributive property.

$(6 n - 4 + 5 (3 n) + 5 \cdot 3) n$

Step 2.1.5

Multiply $3$ by $5$ .

$(6 n - 4 + 15 n + 5 \cdot 3) n$

Step 2.1.6

Multiply $5$ by $3$ .

$(6 n - 4 + 15 n + 15) n$

Step 2.2

Simplify terms.

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Step 2.2.1

Add $6 n$ and $15 n$ .

$(21 n - 4 + 15) n$

Step 2.2.2

Add $- 4$ and $15$ .

$(21 n + 11) n$

Step 2.2.3

Apply the distributive property.

$21 n \cdot n + 11 n$

Step 2.3

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

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Step 2.3.1

Move $n$ .

$21 (n \cdot n) + 11 n$

Step 2.3.2

Multiply $n$ by $n$ .

$21 n^{2} + 11 n$