Finite Math Examples

$r (x) = 400 x$ , $c (x) = x^{2} - 100 x + 3000$

Step 1

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

$(400 x) \cdot (x^{2} - 100 x + 3000)$

Step 2

Simplify.

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Step 2.1

Apply the distributive property.

$400 x \cdot x^{2} + 400 x (- 100 x) + 400 x \cdot 3000$

Step 2.2

Simplify.

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Step 2.2.1

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

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Step 2.2.1.1

Move $x^{2}$ .

$400 (x^{2} x) + 400 x (- 100 x) + 400 x \cdot 3000$

Step 2.2.1.2

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

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Step 2.2.1.2.1

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

$400 (x^{2} x^{1}) + 400 x (- 100 x) + 400 x \cdot 3000$

Step 2.2.1.2.2

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

$400 x^{2 + 1} + 400 x (- 100 x) + 400 x \cdot 3000$

Step 2.2.1.3

Add $2$ and $1$ .

$400 x^{3} + 400 x (- 100 x) + 400 x \cdot 3000$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$400 x^{3} + 400 \cdot - 100 x \cdot x + 400 x \cdot 3000$

Step 2.2.3

Multiply $3000$ by $400$ .

$400 x^{3} + 400 \cdot - 100 x \cdot x + 1200000 x$

Step 2.3

Simplify each term.

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Step 2.3.1

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

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Step 2.3.1.1

Move $x$ .

$400 x^{3} + 400 \cdot - 100 (x \cdot x) + 1200000 x$

Step 2.3.1.2

Multiply $x$ by $x$ .

$400 x^{3} + 400 \cdot - 100 x^{2} + 1200000 x$

Step 2.3.2

Multiply $400$ by $- 100$ .

$400 x^{3} - 40000 x^{2} + 1200000 x$