Finite Math Examples

$R (x) = - x^{2} + 8 x$ , $C (x) = 3 x + 4$

Step 1

Replace the function designators with the actual functions in $R (x) \cdot (C (x))$ .

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

Step 2

Simplify.

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Step 2.1

Expand $(- x^{2} + 8 x) (3 x + 4)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Apply the distributive property.

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

Step 2.1.3

Apply the distributive property.

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

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite using the commutative property of multiplication.

$- 1 \cdot 3 x^{2} x - x^{2} \cdot 4 + 8 x (3 x) + 8 x \cdot 4$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Move $x$ .

$- 1 \cdot 3 (x \cdot x^{2}) - x^{2} \cdot 4 + 8 x (3 x) + 8 x \cdot 4$

Step 2.2.1.2.2

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

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Step 2.2.1.2.2.1

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

$- 1 \cdot 3 (x^{1} x^{2}) - x^{2} \cdot 4 + 8 x (3 x) + 8 x \cdot 4$

Step 2.2.1.2.2.2

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

$- 1 \cdot 3 x^{1 + 2} - x^{2} \cdot 4 + 8 x (3 x) + 8 x \cdot 4$

Step 2.2.1.2.3

Add $1$ and $2$ .

$- 1 \cdot 3 x^{3} - x^{2} \cdot 4 + 8 x (3 x) + 8 x \cdot 4$

Step 2.2.1.3

Multiply $- 1$ by $3$ .

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

Step 2.2.1.4

Multiply $4$ by $- 1$ .

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

Step 2.2.1.5

Rewrite using the commutative property of multiplication.

$- 3 x^{3} - 4 x^{2} + 8 \cdot 3 x \cdot x + 8 x \cdot 4$

Step 2.2.1.6

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1.6.1

Move $x$ .

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

Step 2.2.1.6.2

Multiply $x$ by $x$ .

$- 3 x^{3} - 4 x^{2} + 8 \cdot 3 x^{2} + 8 x \cdot 4$

Step 2.2.1.7

Multiply $8$ by $3$ .

$- 3 x^{3} - 4 x^{2} + 24 x^{2} + 8 x \cdot 4$

Step 2.2.1.8

Multiply $4$ by $8$ .

$- 3 x^{3} - 4 x^{2} + 24 x^{2} + 32 x$

Step 2.2.2

Add $- 4 x^{2}$ and $24 x^{2}$ .

$- 3 x^{3} + 20 x^{2} + 32 x$