Precalculus Examples

$g (a) = 2 a - 1$ $h (a) = 3 a - 3$ Find $(g \cdot h) (- 4)$

Step 1

Evaluate $g \cdot h$ .

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Step 1.1

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

$(2 a - 1) \cdot (3 a - 3)$

Step 1.2

Expand $(2 a - 1) (3 a - 3)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 a (3 a - 3) - 1 (3 a - 3)$

Step 1.2.2

Apply the distributive property.

$2 a (3 a) + 2 a \cdot - 3 - 1 (3 a - 3)$

Step 1.2.3

Apply the distributive property.

$2 a (3 a) + 2 a \cdot - 3 - 1 (3 a) - 1 \cdot - 3$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 a \cdot a + 2 a \cdot - 3 - 1 (3 a) - 1 \cdot - 3$

Step 1.3.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.3.1.2.1

Move $a$ .

$2 \cdot 3 (a \cdot a) + 2 a \cdot - 3 - 1 (3 a) - 1 \cdot - 3$

Step 1.3.1.2.2

Multiply $a$ by $a$ .

$2 \cdot 3 a^{2} + 2 a \cdot - 3 - 1 (3 a) - 1 \cdot - 3$

Step 1.3.1.3

Multiply $2$ by $3$ .

$6 a^{2} + 2 a \cdot - 3 - 1 (3 a) - 1 \cdot - 3$

Step 1.3.1.4

Multiply $- 3$ by $2$ .

$6 a^{2} - 6 a - 1 (3 a) - 1 \cdot - 3$

Step 1.3.1.5

Multiply $3$ by $- 1$ .

$6 a^{2} - 6 a - 3 a - 1 \cdot - 3$

Step 1.3.1.6

Multiply $- 1$ by $- 3$ .

$6 a^{2} - 6 a - 3 a + 3$

Step 1.3.2

Subtract $3 a$ from $- 6 a$ .

$6 a^{2} - 9 a + 3$

Step 2

Evaluate $g \cdot h$ at $- 4$ .

$6 {(- 4)}^{2} - 9 \cdot - 4 + 3$

Step 3

Simplify $6 {(- 4)}^{2} - 9 \cdot - 4 + 3$ .

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Step 3.1

Remove parentheses.

$6 {(- 4)}^{2} - 9 \cdot - 4 + 3$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $- 4$ to the power of $2$ .

$6 \cdot 16 - 9 \cdot - 4 + 3$

Step 3.2.2

Multiply $6$ by $16$ .

$96 - 9 \cdot - 4 + 3$

Step 3.2.3

Multiply $- 9$ by $- 4$ .

$96 + 36 + 3$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $96$ and $36$ .

$132 + 3$

Step 3.3.2

Add $132$ and $3$ .

$135$