Precalculus Examples

$f (x) = - 16 {(\frac{9}{8})}^{2} + 36 (\frac{9}{8})$

Step 1

Apply the product rule to $\frac{9}{8}$ .

$f (x) = - 16 \frac{9^{2}}{8^{2}} + 36 (\frac{9}{8})$

Step 2

Raise $9$ to the power of $2$ .

$f (x) = - 16 \frac{81}{8^{2}} + 36 (\frac{9}{8})$

Step 3

Raise $8$ to the power of $2$ .

$f (x) = - 16 (\frac{81}{64}) + 36 (\frac{9}{8})$

Step 4

Cancel the common factor of $16$ .

Tap for more steps...

Step 4.1

Factor $16$ out of $- 16$ .

$f (x) = 16 (- 1) (\frac{81}{64}) + 36 (\frac{9}{8})$

Step 4.2

Factor $16$ out of $64$ .

$f (x) = 16 \cdot (- 1 \frac{81}{16 \cdot 4}) + 36 (\frac{9}{8})$

Step 4.3

Cancel the common factor.

$f (x) = 16 \cdot (- 1 \frac{81}{16 \cdot 4}) + 36 (\frac{9}{8})$

Step 4.4

Rewrite the expression.

$f (x) = - 1 (\frac{81}{4}) + 36 (\frac{9}{8})$

Step 5

Rewrite $- 1 (\frac{81}{4})$ as $- (\frac{81}{4})$ .

$f (x) = - (\frac{81}{4}) + 36 (\frac{9}{8})$

Step 6

Multiply $- 1$ by $\frac{81}{4}$ .

$f (x) = - \frac{81}{4} + 36 (\frac{9}{8})$

Step 7

Cancel the common factor of $4$ .

Tap for more steps...

Step 7.1

Factor $4$ out of $36$ .

$f (x) = - \frac{81}{4} + 4 (9) (\frac{9}{8})$

Step 7.2

Factor $4$ out of $8$ .

$f (x) = - \frac{81}{4} + 4 \cdot (9 (\frac{9}{4 \cdot 2}))$

Step 7.3

Cancel the common factor.

$f (x) = - \frac{81}{4} + 4 \cdot (9 (\frac{9}{4 \cdot 2}))$

Step 7.4

Rewrite the expression.

$f (x) = - \frac{81}{4} + 9 (\frac{9}{2})$

Step 8

Combine $9$ and $\frac{9}{2}$ .

$f (x) = - \frac{81}{4} + \frac{9 \cdot 9}{2}$

Step 9

Multiply $9$ by $9$ .

$f (x) = - \frac{81}{4} + \frac{81}{2}$

Step 10

To write $\frac{81}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$f (x) = - \frac{81}{4} + \frac{81}{2} \cdot \frac{2}{2}$

Step 11

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 11.1

Multiply $\frac{81}{2}$ by $\frac{2}{2}$ .

$f (x) = - \frac{81}{4} + \frac{81 \cdot 2}{2 \cdot 2}$

Step 11.2

Multiply $2$ by $2$ .

$f (x) = - \frac{81}{4} + \frac{81 \cdot 2}{4}$

Step 12

Combine the numerators over the common denominator.

$f (x) = \frac{- 81 + 81 \cdot 2}{4}$

Step 13

Simplify the numerator.

Tap for more steps...

Step 13.1

Multiply $81$ by $2$ .

$f (x) = \frac{- 81 + 162}{4}$

Step 13.2

Add $- 81$ and $162$ .

$f (x) = \frac{81}{4}$