Algebra Examples

$(12 m^{7} - 8 m^{5} + 16 m^{4} + 6 m^{2}) \div 4 m^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{12 m^{7} - 8 m^{5} + 16 m^{4} + 6 m^{2}}{4 m^{3}}$

Step 2

Factor $2 m^{2}$ out of $12 m^{7} - 8 m^{5} + 16 m^{4} + 6 m^{2}$ .

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Step 2.1

Factor $2 m^{2}$ out of $12 m^{7}$ .

$\frac{2 m^{2} (6 m^{5}) - 8 m^{5} + 16 m^{4} + 6 m^{2}}{4 m^{3}}$

Step 2.2

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

$\frac{2 m^{2} (6 m^{5}) + 2 m^{2} (- 4 m^{3}) + 16 m^{4} + 6 m^{2}}{4 m^{3}}$

Step 2.3

Factor $2 m^{2}$ out of $16 m^{4}$ .

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

Step 2.4

Factor $2 m^{2}$ out of $6 m^{2}$ .

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

Step 2.5

Factor $2 m^{2}$ out of $2 m^{2} (6 m^{5}) + 2 m^{2} (- 4 m^{3})$ .

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

Step 2.6

Factor $2 m^{2}$ out of $2 m^{2} (6 m^{5} - 4 m^{3}) + 2 m^{2} (8 m^{2})$ .

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

Step 2.7

Factor $2 m^{2}$ out of $2 m^{2} (6 m^{5} - 4 m^{3} + 8 m^{2}) + 2 m^{2} (3)$ .

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

Step 3

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

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Step 3.1

Factor $2$ out of $2 m^{2} (6 m^{5} - 4 m^{3} + 8 m^{2} + 3)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $4 m^{3}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factors.

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

Split the fraction $\frac{6 m^{5} - 4 m^{3} + 8 m^{2} + 3}{2 m}$ into two fractions.

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

Step 6

Split the fraction $\frac{6 m^{5} - 4 m^{3} + 8 m^{2}}{2 m}$ into two fractions.

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

Step 7

Split the fraction $\frac{6 m^{5} - 4 m^{3}}{2 m}$ into two fractions.

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

Step 8

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

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Step 8.1

Factor $2$ out of $6 m^{5}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2 m$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$\frac{3 m^{5}}{m} + \frac{- 4 m^{3}}{2 m} + \frac{8 m^{2}}{2 m} + \frac{3}{2 m}$

Step 9

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

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Step 9.1

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

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Raise $m$ to the power of $1$ .

$\frac{m (3 m^{4})}{m^{1}} + \frac{- 4 m^{3}}{2 m} + \frac{8 m^{2}}{2 m} + \frac{3}{2 m}$

Step 9.2.2

Factor $m$ out of $m^{1}$ .

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

Step 9.2.3

Cancel the common factor.

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

Step 9.2.4

Rewrite the expression.

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

Step 9.2.5

Divide $3 m^{4}$ by $1$ .

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

Step 10

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

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Step 10.1

Factor $2$ out of $- 4 m^{3}$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $2 m$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 11

Cancel the common factor of $m^{3}$ and $m$ .

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Step 11.1

Factor $m$ out of $- 2 m^{3}$ .

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Raise $m$ to the power of $1$ .

$3 m^{4} + \frac{m (- 2 m^{2})}{m^{1}} + \frac{8 m^{2}}{2 m} + \frac{3}{2 m}$

Step 11.2.2

Factor $m$ out of $m^{1}$ .

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

Step 11.2.3

Cancel the common factor.

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

Step 11.2.4

Rewrite the expression.

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

Step 11.2.5

Divide $- 2 m^{2}$ by $1$ .

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

Step 12

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

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Step 12.1

Factor $2$ out of $8 m^{2}$ .

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

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $2$ out of $2 m$ .

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

Step 12.2.2

Cancel the common factor.

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

Step 12.2.3

Rewrite the expression.

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

Step 13

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

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Step 13.1

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

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

Step 13.2

Cancel the common factors.

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Step 13.2.1

Raise $m$ to the power of $1$ .

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

Step 13.2.2

Factor $m$ out of $m^{1}$ .

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

Step 13.2.3

Cancel the common factor.

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

Step 13.2.4

Rewrite the expression.

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

Step 13.2.5

Divide $4 m$ by $1$ .

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