Precalculus Examples

$f (x) = 3 x^{2} - 4$ , $5 (f (x + 2))$

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x$ .

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

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.3

Add $1$ and $2$ .

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

Step 2.1.2

Multiply $2$ by $3$ .

$5 (3 x^{3} + 6 x^{2} - 4 x - 4 \cdot 2)$

Step 2.1.3

Multiply $- 4$ by $2$ .

$5 (3 x^{3} + 6 x^{2} - 4 x - 8)$

Step 2.2

Apply the distributive property.

$5 (3 x^{3}) + 5 (6 x^{2}) + 5 (- 4 x) + 5 \cdot - 8$

Step 3

Simplify.

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Step 3.1

Multiply $3$ by $5$ .

$15 x^{3} + 5 (6 x^{2}) + 5 (- 4 x) + 5 \cdot - 8$

Step 3.2

Multiply $6$ by $5$ .

$15 x^{3} + 30 x^{2} + 5 (- 4 x) + 5 \cdot - 8$

Step 3.3

Multiply $- 4$ by $5$ .

$15 x^{3} + 30 x^{2} - 20 x + 5 \cdot - 8$

Step 3.4

Multiply $5$ by $- 8$ .

$15 x^{3} + 30 x^{2} - 20 x - 40$