Precalculus Examples

$g (x) = x^{2} - 3 x$ $h (x) = 2 x - 2$ Find $(g - h) (- 9)$

Step 1

Evaluate $g - h$ .

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Step 1.1

Replace the function designators in $g - h$ with the actual functions.

$(x^{2} - 3 x) - (2 x - 2)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$x^{2} - 3 x - (2 x) - - 2$

Step 1.2.2

Multiply $2$ by $- 1$ .

$x^{2} - 3 x - 2 x - - 2$

Step 1.2.3

Multiply $- 1$ by $- 2$ .

$x^{2} - 3 x - 2 x + 2$

Step 1.3

Subtract $2 x$ from $- 3 x$ .

$x^{2} - 5 x + 2$

Step 2

Evaluate $g - h$ at $- 9$ .

${(- 9)}^{2} - 5 \cdot - 9 + 2$

Step 3

Simplify ${(- 9)}^{2} - 5 \cdot - 9 + 2$ .

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Step 3.1

Remove parentheses.

${(- 9)}^{2} - 5 \cdot - 9 + 2$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $- 9$ to the power of $2$ .

$81 - 5 \cdot - 9 + 2$

Step 3.2.2

Multiply $- 5$ by $- 9$ .

$81 + 45 + 2$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $81$ and $45$ .

$126 + 2$

Step 3.3.2

Add $126$ and $2$ .

$128$