Precalculus Examples

$f (x) = 2 x + 4$ $g (x) = 3 x^{2} - 1$ Find $f (x) \cdot g (x)$

Step 1

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

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

Step 2

Simplify $(2 x + 4) \cdot (3 x^{2} - 1)$ .

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Step 2.1

Expand $(2 x + 4) (3 x^{2} - 1)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

Step 2.2

Simplify terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x^{2}$ .

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

Step 2.2.1.2.2

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

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Step 2.2.1.2.2.1

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

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

Step 2.2.1.2.2.2

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

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

Step 2.2.1.2.3

Add $2$ and $1$ .

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

Step 2.2.1.3

Multiply $2$ by $3$ .

$6 x^{3} + 2 x \cdot - 1 + 4 (3 x^{2}) + 4 \cdot - 1$

Step 2.2.1.4

Multiply $- 1$ by $2$ .

$6 x^{3} - 2 x + 4 (3 x^{2}) + 4 \cdot - 1$

Step 2.2.1.5

Multiply $3$ by $4$ .

$6 x^{3} - 2 x + 12 x^{2} + 4 \cdot - 1$

Step 2.2.1.6

Multiply $4$ by $- 1$ .

$6 x^{3} - 2 x + 12 x^{2} - 4$

Step 2.2.2

Move $- 2 x$ .

$6 x^{3} + 12 x^{2} - 2 x - 4$