Precalculus Examples

$f (x) = 4 x + 8$ $g (x) = x + 3$ find $f (x) \cdot g (x)$

Step 1

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

$(4 x + 8) \cdot (x + 3)$

Step 2

Simplify $(4 x + 8) \cdot (x + 3)$ .

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Step 2.1

Expand $(4 x + 8) (x + 3)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$4 x (x + 3) + 8 (x + 3)$

Step 2.1.2

Apply the distributive property.

$4 x \cdot x + 4 x \cdot 3 + 8 (x + 3)$

Step 2.1.3

Apply the distributive property.

$4 x \cdot x + 4 x \cdot 3 + 8 x + 8 \cdot 3$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1.1.1

Move $x$ .

$4 (x \cdot x) + 4 x \cdot 3 + 8 x + 8 \cdot 3$

Step 2.2.1.1.2

Multiply $x$ by $x$ .

$4 x^{2} + 4 x \cdot 3 + 8 x + 8 \cdot 3$

Step 2.2.1.2

Multiply $3$ by $4$ .

$4 x^{2} + 12 x + 8 x + 8 \cdot 3$

Step 2.2.1.3

Multiply $8$ by $3$ .

$4 x^{2} + 12 x + 8 x + 24$

Step 2.2.2

Add $12 x$ and $8 x$ .

$4 x^{2} + 20 x + 24$