Calculus Examples

$(- \frac{1}{2} Q + 45) (90 - 2 p)$

Step 1

Combine $Q$ and $\frac{1}{2}$ .

$(- \frac{Q}{2} + 45) (90 - 2 p)$

Step 2

Expand $(- \frac{Q}{2} + 45) (90 - 2 p)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- \frac{Q}{2} (90 - 2 p) + 45 (90 - 2 p)$

Step 2.2

Apply the distributive property.

$- \frac{Q}{2} \cdot 90 - \frac{Q}{2} (- 2 p) + 45 (90 - 2 p)$

Step 2.3

Apply the distributive property.

$- \frac{Q}{2} \cdot 90 - \frac{Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Move the leading negative in $- \frac{Q}{2}$ into the numerator.

$\frac{- Q}{2} \cdot 90 - \frac{Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.1.2

Factor $2$ out of $90$ .

$\frac{- Q}{2} \cdot (2 (45)) - \frac{Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.1.3

Cancel the common factor.

$\frac{- Q}{2} \cdot (2 \cdot 45) - \frac{Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.1.4

Rewrite the expression.

$- Q \cdot 45 - \frac{Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.2

Multiply $45$ by $- 1$ .

$- 45 Q - \frac{Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.3

Cancel the common factor of $2$ .

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Step 3.1.3.1

Move the leading negative in $- \frac{Q}{2}$ into the numerator.

$- 45 Q + \frac{- Q}{2} (- 2 p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.3.2

Factor $2$ out of $- 2 p$ .

$- 45 Q + \frac{- Q}{2} (2 (- p)) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.3.3

Cancel the common factor.

$- 45 Q + \frac{- Q}{2} (2 (- p)) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.3.4

Rewrite the expression.

$- 45 Q - Q (- p) + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.4

Multiply $- 1$ by $- 1$ .

$- 45 Q + 1 Q p + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.5

Multiply $Q$ by $1$ .

$- 45 Q + Q p + 45 \cdot 90 + 45 (- 2 p)$

Step 3.1.6

Multiply $45$ by $90$ .

$- 45 Q + Q p + 4050 + 45 (- 2 p)$

Step 3.1.7

Multiply $- 2$ by $45$ .

$- 45 Q + Q p + 4050 - 90 p$

Step 3.2

Simplify the expression.

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Step 3.2.1

Reorder $Q$ and $p$ .

$- 45 Q + p Q + 4050 - 90 p$

Step 3.2.2

Move $4050$ .

$- 45 Q + p Q - 90 p + 4050$

Step 3.2.3

Reorder $- 45 Q$ and $p Q$ .

$p Q - 45 Q - 90 p + 4050$