Precalculus Examples

Given that $f (x) = x^{2} + 9 x + 18$ and $g (x) = x + 6$ ; find $f (x) - g (x)$ and express the result in standard form.

Step 1

Replace the function designators in $f (x) - g x$ with the actual functions.

$(x^{2} + 9 x + 18) - (x + 6)$

Step 2

Simplify $(x^{2} + 9 x + 18) - (x + 6)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x^{2} + 9 x + 18 - x - 1 \cdot 6$

Step 2.1.2

Multiply $- 1$ by $6$ .

$x^{2} + 9 x + 18 - x - 6$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x$ from $9 x$ .

$x^{2} + 8 x + 18 - 6$

Step 2.2.2

Subtract $6$ from $18$ .

$x^{2} + 8 x + 12$