Algebra Examples

$(4 f^{5} - 6 f^{4} + 12 f^{3} - 8 f^{2}) {(4 f^{2})}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(4 f^{5} - 6 f^{4} + 12 f^{3} - 8 f^{2}) \frac{1}{4 f^{2}}$

Step 2

Multiply $4 f^{5} - 6 f^{4} + 12 f^{3} - 8 f^{2}$ by $\frac{1}{4 f^{2}}$ .

$\frac{4 f^{5} - 6 f^{4} + 12 f^{3} - 8 f^{2}}{4 f^{2}}$

Step 3

Factor $2 f^{2}$ out of $4 f^{5} - 6 f^{4} + 12 f^{3} - 8 f^{2}$ .

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Step 3.1

Factor $2 f^{2}$ out of $4 f^{5}$ .

$\frac{2 f^{2} (2 f^{3}) - 6 f^{4} + 12 f^{3} - 8 f^{2}}{4 f^{2}}$

Step 3.2

Factor $2 f^{2}$ out of $- 6 f^{4}$ .

$\frac{2 f^{2} (2 f^{3}) + 2 f^{2} (- 3 f^{2}) + 12 f^{3} - 8 f^{2}}{4 f^{2}}$

Step 3.3

Factor $2 f^{2}$ out of $12 f^{3}$ .

$\frac{2 f^{2} (2 f^{3}) + 2 f^{2} (- 3 f^{2}) + 2 f^{2} (6 f) - 8 f^{2}}{4 f^{2}}$

Step 3.4

Factor $2 f^{2}$ out of $- 8 f^{2}$ .

$\frac{2 f^{2} (2 f^{3}) + 2 f^{2} (- 3 f^{2}) + 2 f^{2} (6 f) + 2 f^{2} (- 4)}{4 f^{2}}$

Step 3.5

Factor $2 f^{2}$ out of $2 f^{2} (2 f^{3}) + 2 f^{2} (- 3 f^{2})$ .

$\frac{2 f^{2} (2 f^{3} - 3 f^{2}) + 2 f^{2} (6 f) + 2 f^{2} (- 4)}{4 f^{2}}$

Step 3.6

Factor $2 f^{2}$ out of $2 f^{2} (2 f^{3} - 3 f^{2}) + 2 f^{2} (6 f)$ .

$\frac{2 f^{2} (2 f^{3} - 3 f^{2} + 6 f) + 2 f^{2} (- 4)}{4 f^{2}}$

Step 3.7

Factor $2 f^{2}$ out of $2 f^{2} (2 f^{3} - 3 f^{2} + 6 f) + 2 f^{2} (- 4)$ .

$\frac{2 f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4)}{4 f^{2}}$

Step 4

Cancel the common factor of $2$ and $4$ .

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Step 4.1

Factor $2$ out of $2 f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4)$ .

$\frac{2 (f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4))}{4 f^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $4 f^{2}$ .

$\frac{2 (f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4))}{2 (2 f^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4))}{2 (2 f^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4)}{2 f^{2}}$

Step 5

Cancel the common factor of $f^{2}$ .

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Step 5.1

Cancel the common factor.

$\frac{f^{2} (2 f^{3} - 3 f^{2} + 6 f - 4)}{2 f^{2}}$

Step 5.2

Rewrite the expression.

$\frac{2 f^{3} - 3 f^{2} + 6 f - 4}{2}$

Step 6

Split the fraction $\frac{2 f^{3} - 3 f^{2} + 6 f - 4}{2}$ into two fractions.

$\frac{2 f^{3} - 3 f^{2} + 6 f}{2} + \frac{- 4}{2}$

Step 7

Split the fraction $\frac{2 f^{3} - 3 f^{2} + 6 f}{2}$ into two fractions.

$\frac{2 f^{3} - 3 f^{2}}{2} + \frac{6 f}{2} + \frac{- 4}{2}$

Step 8

Split the fraction $\frac{2 f^{3} - 3 f^{2}}{2}$ into two fractions.

$\frac{2 f^{3}}{2} + \frac{- 3 f^{2}}{2} + \frac{6 f}{2} + \frac{- 4}{2}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Cancel the common factor.

$\frac{2 f^{3}}{2} + \frac{- 3 f^{2}}{2} + \frac{6 f}{2} + \frac{- 4}{2}$

Step 9.2

Divide $f^{3}$ by $1$ .

$f^{3} + \frac{- 3 f^{2}}{2} + \frac{6 f}{2} + \frac{- 4}{2}$

Step 10

Move the negative in front of the fraction.

$f^{3} - \frac{3 f^{2}}{2} + \frac{6 f}{2} + \frac{- 4}{2}$

Step 11

Cancel the common factor of $6$ and $2$ .

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Step 11.1

Factor $2$ out of $6 f$ .

$f^{3} - \frac{3 f^{2}}{2} + \frac{2 (3 f)}{2} + \frac{- 4}{2}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $2$ out of $2$ .

$f^{3} - \frac{3 f^{2}}{2} + \frac{2 (3 f)}{2 (1)} + \frac{- 4}{2}$

Step 11.2.2

Cancel the common factor.

$f^{3} - \frac{3 f^{2}}{2} + \frac{2 (3 f)}{2 \cdot 1} + \frac{- 4}{2}$

Step 11.2.3

Rewrite the expression.

$f^{3} - \frac{3 f^{2}}{2} + \frac{3 f}{1} + \frac{- 4}{2}$

Step 11.2.4

Divide $3 f$ by $1$ .

$f^{3} - \frac{3 f^{2}}{2} + 3 f + \frac{- 4}{2}$

Step 12

Divide $- 4$ by $2$ .

$f^{3} - \frac{3 f^{2}}{2} + 3 f - 2$