Precalculus Examples

$g (t) = t^{2} + 3$ $h (t) = 4 t - 3$ find $(g \cdot h) (- 1)$

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.

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

Step 1.2

Expand $(t^{2} + 3) (4 t - 3)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$t^{2} (4 t - 3) + 3 (4 t - 3)$

Step 1.2.2

Apply the distributive property.

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

Step 1.2.3

Apply the distributive property.

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

Step 1.3

Simplify each term.

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Step 1.3.1

Rewrite using the commutative property of multiplication.

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

Step 1.3.2

Multiply $t^{2}$ by $t$ by adding the exponents.

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Step 1.3.2.1

Move $t$ .

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

Step 1.3.2.2

Multiply $t$ by $t^{2}$ .

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Step 1.3.2.2.1

Raise $t$ to the power of $1$ .

$4 (t^{1} t^{2}) + t^{2} \cdot - 3 + 3 (4 t) + 3 \cdot - 3$

Step 1.3.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 t^{1 + 2} + t^{2} \cdot - 3 + 3 (4 t) + 3 \cdot - 3$

Step 1.3.2.3

Add $1$ and $2$ .

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

Step 1.3.3

Move $- 3$ to the left of $t^{2}$ .

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

Step 1.3.4

Multiply $4$ by $3$ .

$4 t^{3} - 3 t^{2} + 12 t + 3 \cdot - 3$

Step 1.3.5

Multiply $3$ by $- 3$ .

$4 t^{3} - 3 t^{2} + 12 t - 9$

Step 2

Evaluate $g \cdot h$ at $- 1$ .

$4 {(- 1)}^{3} - 3 {(- 1)}^{2} + 12 (- 1) - 9$

Step 3

Simplify $4 {(- 1)}^{3} - 3 {(- 1)}^{2} + 12 (- 1) - 9$ .

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Step 3.1

Remove parentheses.

$4 {(- 1)}^{3} - 3 {(- 1)}^{2} + 12 (- 1) - 9$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $- 1$ to the power of $3$ .

$4 \cdot - 1 - 3 {(- 1)}^{2} + 12 (- 1) - 9$

Step 3.2.2

Multiply $4$ by $- 1$ .

$- 4 - 3 {(- 1)}^{2} + 12 (- 1) - 9$

Step 3.2.3

Raise $- 1$ to the power of $2$ .

$- 4 - 3 \cdot 1 + 12 (- 1) - 9$

Step 3.2.4

Multiply $- 3$ by $1$ .

$- 4 - 3 + 12 (- 1) - 9$

Step 3.2.5

Multiply $12$ by $- 1$ .

$- 4 - 3 - 12 - 9$

Step 3.3

Simplify by subtracting numbers.

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Step 3.3.1

Subtract $3$ from $- 4$ .

$- 7 - 12 - 9$

Step 3.3.2

Subtract $12$ from $- 7$ .

$- 19 - 9$

Step 3.3.3

Subtract $9$ from $- 19$ .

$- 28$