Finite Math Examples

$r (x) = 8 x - 0.001 x^{2}$ , $c (x) = 5 x$

Step 1

Replace the function designators with the actual functions in $r (x) \cdot (c (x))$ .

$(8 x - 0.001 x^{2}) \cdot (5 x)$

Step 2

Simplify.

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Step 2.1

Simplify by multiplying through.

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Step 2.1.1

Apply the distributive property.

$8 x (5 x) - 0.001 x^{2} (5 x)$

Step 2.1.2

Reorder.

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Step 2.1.2.1

Rewrite using the commutative property of multiplication.

$8 \cdot 5 x \cdot x - 0.001 x^{2} (5 x)$

Step 2.1.2.2

Rewrite using the commutative property of multiplication.

$8 \cdot 5 x \cdot x - 0.001 \cdot 5 x^{2} x$

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

Move $x$ .

$8 \cdot 5 (x \cdot x) - 0.001 \cdot 5 x^{2} x$

Step 2.2.1.2

Multiply $x$ by $x$ .

$8 \cdot 5 x^{2} - 0.001 \cdot 5 x^{2} x$

Step 2.2.2

Multiply $8$ by $5$ .

$40 x^{2} - 0.001 \cdot 5 x^{2} x$

Step 2.2.3

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

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Step 2.2.3.1

Move $x$ .

$40 x^{2} - 0.001 \cdot 5 (x \cdot x^{2})$

Step 2.2.3.2

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

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Step 2.2.3.2.1

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

$40 x^{2} - 0.001 \cdot 5 (x^{1} x^{2})$

Step 2.2.3.2.2

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

$40 x^{2} - 0.001 \cdot 5 x^{1 + 2}$

Step 2.2.3.3

Add $1$ and $2$ .

$40 x^{2} - 0.001 \cdot 5 x^{3}$

Step 2.2.4

Multiply $- 0.001$ by $5$ .

$40 x^{2} - 0.005 x^{3}$