Algebra Examples

$\frac{8 y^{10} - 2 y^{6} + 5 y^{3} + 9 y}{2 y^{3}}$

Step 1

Factor $y$ out of $8 y^{10} - 2 y^{6} + 5 y^{3} + 9 y$ .

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Step 1.1

Factor $y$ out of $8 y^{10}$ .

$\frac{y (8 y^{9}) - 2 y^{6} + 5 y^{3} + 9 y}{2 y^{3}}$

Step 1.2

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

$\frac{y (8 y^{9}) + y (- 2 y^{5}) + 5 y^{3} + 9 y}{2 y^{3}}$

Step 1.3

Factor $y$ out of $5 y^{3}$ .

$\frac{y (8 y^{9}) + y (- 2 y^{5}) + y (5 y^{2}) + 9 y}{2 y^{3}}$

Step 1.4

Factor $y$ out of $9 y$ .

$\frac{y (8 y^{9}) + y (- 2 y^{5}) + y (5 y^{2}) + y \cdot 9}{2 y^{3}}$

Step 1.5

Factor $y$ out of $y (8 y^{9}) + y (- 2 y^{5})$ .

$\frac{y (8 y^{9} - 2 y^{5}) + y (5 y^{2}) + y \cdot 9}{2 y^{3}}$

Step 1.6

Factor $y$ out of $y (8 y^{9} - 2 y^{5}) + y (5 y^{2})$ .

$\frac{y (8 y^{9} - 2 y^{5} + 5 y^{2}) + y \cdot 9}{2 y^{3}}$

Step 1.7

Factor $y$ out of $y (8 y^{9} - 2 y^{5} + 5 y^{2}) + y \cdot 9$ .

$\frac{y (8 y^{9} - 2 y^{5} + 5 y^{2} + 9)}{2 y^{3}}$

Step 2

Cancel the common factors.

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Step 2.1

Factor $y$ out of $2 y^{3}$ .

$\frac{y (8 y^{9} - 2 y^{5} + 5 y^{2} + 9)}{y (2 y^{2})}$

Step 2.2

Cancel the common factor.

$\frac{y (8 y^{9} - 2 y^{5} + 5 y^{2} + 9)}{y (2 y^{2})}$

Step 2.3

Rewrite the expression.

$\frac{8 y^{9} - 2 y^{5} + 5 y^{2} + 9}{2 y^{2}}$

Step 3

Split the fraction $\frac{8 y^{9} - 2 y^{5} + 5 y^{2} + 9}{2 y^{2}}$ into two fractions.

$\frac{8 y^{9} - 2 y^{5} + 5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 4

Split the fraction $\frac{8 y^{9} - 2 y^{5} + 5 y^{2}}{2 y^{2}}$ into two fractions.

$\frac{8 y^{9} - 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 5

Split the fraction $\frac{8 y^{9} - 2 y^{5}}{2 y^{2}}$ into two fractions.

$\frac{8 y^{9}}{2 y^{2}} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 6

Cancel the common factor of $8$ and $2$ .

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Step 6.1

Factor $2$ out of $8 y^{9}$ .

$\frac{2 (4 y^{9})}{2 y^{2}} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 y^{2}$ .

$\frac{2 (4 y^{9})}{2 (y^{2})} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (4 y^{9})}{2 y^{2}} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 6.2.3

Rewrite the expression.

$\frac{4 y^{9}}{y^{2}} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 7

Cancel the common factor of $y^{9}$ and $y^{2}$ .

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Step 7.1

Factor $y^{2}$ out of $4 y^{9}$ .

$\frac{y^{2} (4 y^{7})}{y^{2}} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Multiply by $1$ .

$\frac{y^{2} (4 y^{7})}{y^{2} \cdot 1} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 7.2.2

Cancel the common factor.

$\frac{y^{2} (4 y^{7})}{y^{2} \cdot 1} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 7.2.3

Rewrite the expression.

$\frac{4 y^{7}}{1} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 7.2.4

Divide $4 y^{7}$ by $1$ .

$4 y^{7} + \frac{- 2 y^{5}}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 8

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

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Step 8.1

Factor $2$ out of $- 2 y^{5}$ .

$4 y^{7} + \frac{2 (- y^{5})}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2 y^{2}$ .

$4 y^{7} + \frac{2 (- y^{5})}{2 (y^{2})} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 8.2.2

Cancel the common factor.

$4 y^{7} + \frac{2 (- y^{5})}{2 y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 8.2.3

Rewrite the expression.

$4 y^{7} + \frac{- y^{5}}{y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 9

Cancel the common factor of $y^{5}$ and $y^{2}$ .

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Step 9.1

Factor $y^{2}$ out of $- y^{5}$ .

$4 y^{7} + \frac{y^{2} (- y^{3})}{y^{2}} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

$4 y^{7} + \frac{y^{2} (- y^{3})}{y^{2} \cdot 1} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 9.2.2

Cancel the common factor.

$4 y^{7} + \frac{y^{2} (- y^{3})}{y^{2} \cdot 1} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 9.2.3

Rewrite the expression.

$4 y^{7} + \frac{- y^{3}}{1} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 9.2.4

Divide $- y^{3}$ by $1$ .

$4 y^{7} - y^{3} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 10

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

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Step 10.1

Cancel the common factor.

$4 y^{7} - y^{3} + \frac{5 y^{2}}{2 y^{2}} + \frac{9}{2 y^{2}}$

Step 10.2

Rewrite the expression.

$4 y^{7} - y^{3} + \frac{5}{2} + \frac{9}{2 y^{2}}$