Finite Math Examples

$f (x) = 6 x$ , $g (x) = 8 x^{2} + 8$ , $(g \cdot f) (2)$

Step 1

Evaluate $g \cdot f$ .

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Step 1.1

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

$(8 x^{2} + 8) \cdot (6 x)$

Step 1.2

Simplify by multiplying through.

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Step 1.2.1

Apply the distributive property.

$8 x^{2} (6 x) + 8 (6 x)$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Rewrite using the commutative property of multiplication.

$8 \cdot 6 x^{2} x + 8 (6 x)$

Step 1.2.2.2

Multiply $6$ by $8$ .

$8 \cdot 6 x^{2} x + 48 x$

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 $x$ .

$8 \cdot 6 (x \cdot x^{2}) + 48 x$

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 $1$ .

$8 \cdot 6 (x^{1} x^{2}) + 48 x$

Step 1.3.1.2.2

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

$8 \cdot 6 x^{1 + 2} + 48 x$

Step 1.3.1.3

Add $1$ and $2$ .

$8 \cdot 6 x^{3} + 48 x$

Step 1.3.2

Multiply $8$ by $6$ .

$48 x^{3} + 48 x$

Step 2

Evaluate $g \cdot f$ at $2$ .

$48 {(2)}^{3} + 48 (2)$

Step 3

Simplify $48 {(2)}^{3} + 48 (2)$ .

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Step 3.1

Remove parentheses.

$48 {(2)}^{3} + 48 (2)$

Step 3.2

Simplify each term.

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Step 3.2.1

Raise $2$ to the power of $3$ .

$48 \cdot 8 + 48 (2)$

Step 3.2.2

Multiply $48$ by $8$ .

$384 + 48 (2)$

Step 3.2.3

Multiply $48$ by $2$ .

$384 + 96$

Step 3.3

Add $384$ and $96$ .

$480$