Finite Math Examples

$f (x) = 2 x^{2} - 2$ , $g (x) = - 2 x$ , $(f g) (x)$

Step 1

Evaluate $f g$ .

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Step 1.1

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

$(2 x^{2} - 2) (- 2 x)$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$2 x^{2} (- 2 x) - 2 (- 2 x)$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot - 2 x^{2} x - 2 (- 2 x)$

Step 1.2.2.2

Multiply $- 2$ by $- 2$ .

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

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x$ .

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

Step 1.3.1.2

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

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Step 1.3.1.2.1

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

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

Step 1.3.1.2.2

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

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

Step 1.3.1.3

Add $1$ and $2$ .

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

Step 1.3.2

Multiply $2$ by $- 2$ .

$- 4 x^{3} + 4 x$

Step 2

Evaluate $f g$ at $x$ .

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

Step 3

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

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Step 3.1

Remove parentheses.

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

Step 3.2

Multiply $4$ by $x$ .

$- 4 x^{3} + 4 x$