Precalculus Examples

$(f \cdot g) (4)$ , $f (x) = 2 x + 3$ , $g (x) = x^{2} + 5 x$

Step 1

Evaluate $f \cdot g$ .

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Step 1.1

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

$(2 x + 3) \cdot (x^{2} + 5 x)$

Step 1.2

Expand $(2 x + 3) (x^{2} + 5 x)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 x (x^{2} + 5 x) + 3 (x^{2} + 5 x)$

Step 1.2.2

Apply the distributive property.

$2 x \cdot x^{2} + 2 x (5 x) + 3 (x^{2} + 5 x)$

Step 1.2.3

Apply the distributive property.

$2 x \cdot x^{2} + 2 x (5 x) + 3 x^{2} + 3 (5 x)$

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

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

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Step 1.3.1.1.1

Move $x^{2}$ .

$2 (x^{2} x) + 2 x (5 x) + 3 x^{2} + 3 (5 x)$

Step 1.3.1.1.2

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

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Step 1.3.1.1.2.1

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

$2 (x^{2} x^{1}) + 2 x (5 x) + 3 x^{2} + 3 (5 x)$

Step 1.3.1.1.2.2

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

$2 x^{2 + 1} + 2 x (5 x) + 3 x^{2} + 3 (5 x)$

Step 1.3.1.1.3

Add $2$ and $1$ .

$2 x^{3} + 2 x (5 x) + 3 x^{2} + 3 (5 x)$

Step 1.3.1.2

Rewrite using the commutative property of multiplication.

$2 x^{3} + 2 \cdot 5 x \cdot x + 3 x^{2} + 3 (5 x)$

Step 1.3.1.3

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

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Step 1.3.1.3.1

Move $x$ .

$2 x^{3} + 2 \cdot 5 (x \cdot x) + 3 x^{2} + 3 (5 x)$

Step 1.3.1.3.2

Multiply $x$ by $x$ .

$2 x^{3} + 2 \cdot 5 x^{2} + 3 x^{2} + 3 (5 x)$

Step 1.3.1.4

Multiply $2$ by $5$ .

$2 x^{3} + 10 x^{2} + 3 x^{2} + 3 (5 x)$

Step 1.3.1.5

Multiply $5$ by $3$ .

$2 x^{3} + 10 x^{2} + 3 x^{2} + 15 x$

Step 1.3.2

Add $10 x^{2}$ and $3 x^{2}$ .

$2 x^{3} + 13 x^{2} + 15 x$

Step 2

Evaluate $f \cdot g$ at $4$ .

$2 {(4)}^{3} + 13 {(4)}^{2} + 15 (4)$

Step 3

Simplify $2 {(4)}^{3} + 13 {(4)}^{2} + 15 (4)$ .

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Step 3.1

Remove parentheses.

$2 {(4)}^{3} + 13 {(4)}^{2} + 15 (4)$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $4$ to the power of $3$ .

$2 \cdot 64 + 13 {(4)}^{2} + 15 (4)$

Step 3.2.2

Multiply $2$ by $64$ .

$128 + 13 {(4)}^{2} + 15 (4)$

Step 3.2.3

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

$128 + 13 \cdot 16 + 15 (4)$

Step 3.2.4

Multiply $13$ by $16$ .

$128 + 208 + 15 (4)$

Step 3.2.5

Multiply $15$ by $4$ .

$128 + 208 + 60$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $128$ and $208$ .

$336 + 60$

Step 3.3.2

Add $336$ and $60$ .

$396$