Finite Math Examples

$S (p) = 9 p + 12$ , $D (p) = 280 - 9 p$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in $S (p) \cdot (D (p))$ .

$(9 p + 12) \cdot (280 - 9 p)$

Step 1.2

Simplify.

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Step 1.2.1

Expand $(9 p + 12) (280 - 9 p)$ using the FOIL Method.

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Step 1.2.1.1

Apply the distributive property.

$9 p (280 - 9 p) + 12 (280 - 9 p)$

Step 1.2.1.2

Apply the distributive property.

$9 p \cdot 280 + 9 p (- 9 p) + 12 (280 - 9 p)$

Step 1.2.1.3

Apply the distributive property.

$9 p \cdot 280 + 9 p (- 9 p) + 12 \cdot 280 + 12 (- 9 p)$

Step 1.2.2

Simplify and combine like terms.

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Step 1.2.2.1

Simplify each term.

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Step 1.2.2.1.1

Multiply $280$ by $9$ .

$2520 p + 9 p (- 9 p) + 12 \cdot 280 + 12 (- 9 p)$

Step 1.2.2.1.2

Rewrite using the commutative property of multiplication.

$2520 p + 9 \cdot - 9 p \cdot p + 12 \cdot 280 + 12 (- 9 p)$

Step 1.2.2.1.3

Multiply $p$ by $p$ by adding the exponents.

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Step 1.2.2.1.3.1

Move $p$ .

$2520 p + 9 \cdot - 9 (p \cdot p) + 12 \cdot 280 + 12 (- 9 p)$

Step 1.2.2.1.3.2

Multiply $p$ by $p$ .

$2520 p + 9 \cdot - 9 p^{2} + 12 \cdot 280 + 12 (- 9 p)$

Step 1.2.2.1.4

Multiply $9$ by $- 9$ .

$2520 p - 81 p^{2} + 12 \cdot 280 + 12 (- 9 p)$

Step 1.2.2.1.5

Multiply $12$ by $280$ .

$2520 p - 81 p^{2} + 3360 + 12 (- 9 p)$

Step 1.2.2.1.6

Multiply $- 9$ by $12$ .

$2520 p - 81 p^{2} + 3360 - 108 p$

Step 1.2.2.2

Subtract $108 p$ from $2520 p$ .

$2412 p - 81 p^{2} + 3360$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3