Algebra Examples

$\frac{15 r^{10} - 5 r^{8} + 40 r^{2}}{5 r^{4}}$

Step 1

Factor $5 r^{2}$ out of $15 r^{10} - 5 r^{8} + 40 r^{2}$ .

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Step 1.1

Factor $5 r^{2}$ out of $15 r^{10}$ .

$\frac{5 r^{2} (3 r^{8}) - 5 r^{8} + 40 r^{2}}{5 r^{4}}$

Step 1.2

Factor $5 r^{2}$ out of $- 5 r^{8}$ .

$\frac{5 r^{2} (3 r^{8}) + 5 r^{2} (- r^{6}) + 40 r^{2}}{5 r^{4}}$

Step 1.3

Factor $5 r^{2}$ out of $40 r^{2}$ .

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

Step 1.4

Factor $5 r^{2}$ out of $5 r^{2} (3 r^{8}) + 5 r^{2} (- r^{6})$ .

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

Step 1.5

Factor $5 r^{2}$ out of $5 r^{2} (3 r^{8} - r^{6}) + 5 r^{2} (8)$ .

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

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factors.

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{3 r^{8} - r^{6} + 8}{r^{2}}$

Step 4

Split the fraction $\frac{3 r^{8} - r^{6} + 8}{r^{2}}$ into two fractions.

$\frac{3 r^{8} - r^{6}}{r^{2}} + \frac{8}{r^{2}}$

Step 5

Split the fraction $\frac{3 r^{8} - r^{6}}{r^{2}}$ into two fractions.

$\frac{3 r^{8}}{r^{2}} + \frac{- r^{6}}{r^{2}} + \frac{8}{r^{2}}$

Step 6

Cancel the common factor of $r^{8}$ and $r^{2}$ .

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Step 6.1

Factor $r^{2}$ out of $3 r^{8}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Multiply by $1$ .

$\frac{r^{2} (3 r^{6})}{r^{2} \cdot 1} + \frac{- r^{6}}{r^{2}} + \frac{8}{r^{2}}$

Step 6.2.2

Cancel the common factor.

$\frac{r^{2} (3 r^{6})}{r^{2} \cdot 1} + \frac{- r^{6}}{r^{2}} + \frac{8}{r^{2}}$

Step 6.2.3

Rewrite the expression.

$\frac{3 r^{6}}{1} + \frac{- r^{6}}{r^{2}} + \frac{8}{r^{2}}$

Step 6.2.4

Divide $3 r^{6}$ by $1$ .

$3 r^{6} + \frac{- r^{6}}{r^{2}} + \frac{8}{r^{2}}$

Step 7

Cancel the common factor of $r^{6}$ and $r^{2}$ .

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Step 7.1

Factor $r^{2}$ out of $- r^{6}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Multiply by $1$ .

$3 r^{6} + \frac{r^{2} (- r^{4})}{r^{2} \cdot 1} + \frac{8}{r^{2}}$

Step 7.2.2

Cancel the common factor.

$3 r^{6} + \frac{r^{2} (- r^{4})}{r^{2} \cdot 1} + \frac{8}{r^{2}}$

Step 7.2.3

Rewrite the expression.

$3 r^{6} + \frac{- r^{4}}{1} + \frac{8}{r^{2}}$

Step 7.2.4

Divide $- r^{4}$ by $1$ .

$3 r^{6} - r^{4} + \frac{8}{r^{2}}$