Basic Math Examples

$\frac{- 8 f}{10 f - 8} \cdot \frac{5 f^{2} + 4 f - 6}{10 f - 8}$

Step 1

Factor $2$ out of $10 f - 8$ .

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Step 1.1

Factor $2$ out of $10 f$ .

$\frac{- 8 f}{2 (5 f) - 8} \cdot \frac{5 f^{2} + 4 f - 6}{10 f - 8}$

Step 1.2

Factor $2$ out of $- 8$ .

$\frac{- 8 f}{2 (5 f) + 2 (- 4)} \cdot \frac{5 f^{2} + 4 f - 6}{10 f - 8}$

Step 1.3

Factor $2$ out of $2 (5 f) + 2 (- 4)$ .

$\frac{- 8 f}{2 (5 f - 4)} \cdot \frac{5 f^{2} + 4 f - 6}{10 f - 8}$

Step 2

Factor $2$ out of $10 f - 8$ .

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Step 2.1

Factor $2$ out of $10 f$ .

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

Step 2.2

Factor $2$ out of $- 8$ .

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

Step 2.3

Factor $2$ out of $2 (5 f) + 2 (- 4)$ .

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $- 8 f$ .

$\frac{2 (- 4 f)}{2 (5 f - 4)} \cdot \frac{5 f^{2} + 4 f - 6}{2 (5 f - 4)}$

Step 3.2

Cancel the common factor.

$\frac{2 (- 4 f)}{2 (5 f - 4)} \cdot \frac{5 f^{2} + 4 f - 6}{2 (5 f - 4)}$

Step 3.3

Rewrite the expression.

$\frac{- 4 f}{2 (5 f - 4)} \cdot \frac{5 f^{2} + 4 f - 6}{5 f - 4}$

Step 4

Multiply $\frac{- 4 f}{2 (5 f - 4)}$ by $\frac{5 f^{2} + 4 f - 6}{5 f - 4}$ .

$\frac{- 4 f (5 f^{2} + 4 f - 6)}{2 (5 f - 4) (5 f - 4)}$

Step 5

Raise $5 f - 4$ to the power of $1$ .

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

Step 6

Raise $5 f - 4$ to the power of $1$ .

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

Step 7

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

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

Step 8

Add $1$ and $1$ .

$\frac{- 4 f (5 f^{2} + 4 f - 6)}{2 {(5 f - 4)}^{2}}$

Step 9

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

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Step 9.1

Factor $2$ out of $- 4 f (5 f^{2} + 4 f - 6)$ .

$\frac{2 (- 2 f (5 f^{2} + 4 f - 6))}{2 {(5 f - 4)}^{2}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

$\frac{2 (- 2 f (5 f^{2} + 4 f - 6))}{2 ({(5 f - 4)}^{2})}$

Step 9.2.2

Cancel the common factor.

$\frac{2 (- 2 f (5 f^{2} + 4 f - 6))}{2 {(5 f - 4)}^{2}}$

Step 9.2.3

Rewrite the expression.

$\frac{- 2 f (5 f^{2} + 4 f - 6)}{{(5 f - 4)}^{2}}$

Step 10

Move the negative in front of the fraction.

$- \frac{2 f (5 f^{2} + 4 f - 6)}{{(5 f - 4)}^{2}}$