Algebra Examples

$f (x) = 3 x + 1$ , $g (x) = x^{2} - 6$

Step 1

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

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

Step 2

Simplify.

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Step 2.1

Expand $(3 x + 1) (x^{2} - 6)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

Move $x^{2}$ .

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

Step 2.2.1.2

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

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Step 2.2.1.2.1

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

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

Step 2.2.1.2.2

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

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

Step 2.2.1.3

Add $2$ and $1$ .

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

Step 2.2.2

Multiply $- 6$ by $3$ .

$3 x^{3} - 18 x + 1 x^{2} + 1 \cdot - 6$

Step 2.2.3

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

$3 x^{3} - 18 x + x^{2} + 1 \cdot - 6$

Step 2.2.4

Multiply $- 6$ by $1$ .

$3 x^{3} - 18 x + x^{2} - 6$