Precalculus Examples

Find $(g - h) (x)$ when $g (x) = x^{3} + 2 x^{2} - 8 x$ and $h (x) = - 3 x^{3} + 6 x^{2} + 5 x - 9$

Step 1

Evaluate $g - h$ .

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Step 1.1

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

$(x^{3} + 2 x^{2} - 8 x) - (- 3 x^{3} + 6 x^{2} + 5 x - 9)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$x^{3} + 2 x^{2} - 8 x - (- 3 x^{3}) - (6 x^{2}) - (5 x) - - 9$

Step 1.2.2

Simplify.

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Step 1.2.2.1

Multiply $- 3$ by $- 1$ .

$x^{3} + 2 x^{2} - 8 x + 3 x^{3} - (6 x^{2}) - (5 x) - - 9$

Step 1.2.2.2

Multiply $6$ by $- 1$ .

$x^{3} + 2 x^{2} - 8 x + 3 x^{3} - 6 x^{2} - (5 x) - - 9$

Step 1.2.2.3

Multiply $5$ by $- 1$ .

$x^{3} + 2 x^{2} - 8 x + 3 x^{3} - 6 x^{2} - 5 x - - 9$

Step 1.2.2.4

Multiply $- 1$ by $- 9$ .

$x^{3} + 2 x^{2} - 8 x + 3 x^{3} - 6 x^{2} - 5 x + 9$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Add $x^{3}$ and $3 x^{3}$ .

$4 x^{3} + 2 x^{2} - 8 x - 6 x^{2} - 5 x + 9$

Step 1.3.2

Subtract $6 x^{2}$ from $2 x^{2}$ .

$4 x^{3} - 4 x^{2} - 8 x - 5 x + 9$

Step 1.3.3

Subtract $5 x$ from $- 8 x$ .

$4 x^{3} - 4 x^{2} - 13 x + 9$

Step 2

Evaluate $g - h$ at $x$ .

$4 {(x)}^{3} - 4 {(x)}^{2} - 13 x + 9$

Step 3

Simplify $4 {(x)}^{3} - 4 {(x)}^{2} - 13 x + 9$ .

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Step 3.1

Remove parentheses.

$4 {(x)}^{3} - 4 {(x)}^{2} - 13 x + 9$

Step 3.2

Remove parentheses.

$4 x^{3} - 4 x^{2} - 13 x + 9$