Algebra Examples

$f (x) = 4 x + 1$ , $g (x) = x^{2} - 5$ , $(f \cdot g) (x)$

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.

$(4 x + 1) \cdot (x^{2} - 5)$

Step 1.2

Expand $(4 x + 1) (x^{2} - 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$4 x (x^{2} - 5) + 1 (x^{2} - 5)$

Step 1.2.2

Apply the distributive property.

$4 x \cdot x^{2} + 4 x \cdot - 5 + 1 (x^{2} - 5)$

Step 1.2.3

Apply the distributive property.

$4 x \cdot x^{2} + 4 x \cdot - 5 + 1 x^{2} + 1 \cdot - 5$

Step 1.3

Simplify 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 $x^{2}$ .

$4 (x^{2} x) + 4 x \cdot - 5 + 1 x^{2} + 1 \cdot - 5$

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 $1$ .

$4 (x^{2} x^{1}) + 4 x \cdot - 5 + 1 x^{2} + 1 \cdot - 5$

Step 1.3.1.1.2.2

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

$4 x^{2 + 1} + 4 x \cdot - 5 + 1 x^{2} + 1 \cdot - 5$

Step 1.3.1.1.3

Add $2$ and $1$ .

$4 x^{3} + 4 x \cdot - 5 + 1 x^{2} + 1 \cdot - 5$

Step 1.3.1.2

Multiply $- 5$ by $4$ .

$4 x^{3} - 20 x + 1 x^{2} + 1 \cdot - 5$

Step 1.3.1.3

Multiply $x^{2}$ by $1$ .

$4 x^{3} - 20 x + x^{2} + 1 \cdot - 5$

Step 1.3.1.4

Multiply $- 5$ by $1$ .

$4 x^{3} - 20 x + x^{2} - 5$

Step 1.3.2

Move $- 20 x$ .

$4 x^{3} + x^{2} - 20 x - 5$

Step 2

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

$4 {(x)}^{3} + {(x)}^{2} - 20 x - 5$

Step 3

Simplify $4 {(x)}^{3} + {(x)}^{2} - 20 x - 5$ .

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Step 3.1

Remove parentheses.

$4 {(x)}^{3} + {(x)}^{2} - 20 x - 5$

Step 3.2

Remove parentheses.

$4 x^{3} + x^{2} - 20 x - 5$