Algebra Examples

$\frac{24 m n^{6} - 40 m^{2} n^{3}}{4 m^{2} n^{3}}$

Step 1

Factor $8 m n^{3}$ out of $24 m n^{6} - 40 m^{2} n^{3}$ .

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Step 1.1

Factor $8 m n^{3}$ out of $24 m n^{6}$ .

$\frac{8 m n^{3} (3 n^{3}) - 40 m^{2} n^{3}}{4 m^{2} n^{3}}$

Step 1.2

Factor $8 m n^{3}$ out of $- 40 m^{2} n^{3}$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $8$ and $4$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{2 m n^{3} (3 n^{3} - 5 m)}{m^{2} n^{3}}$

Step 3

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

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Step 3.1

Factor $m$ out of $2 m n^{3} (3 n^{3} - 5 m)$ .

$\frac{m (2 n^{3} (3 n^{3} - 5 m))}{m^{2} n^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{m (2 n^{3} (3 n^{3} - 5 m))}{m (m n^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{m (2 n^{3} (3 n^{3} - 5 m))}{m (m n^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 n^{3} (3 n^{3} - 5 m)}{m n^{3}}$

Step 4

Cancel the common factor of $n^{3}$ .

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Step 4.1

Cancel the common factor.

$\frac{2 n^{3} (3 n^{3} - 5 m)}{m n^{3}}$

Step 4.2

Rewrite the expression.

$\frac{2 (3 n^{3} - 5 m)}{m}$

Step 5

Apply the distributive property.

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

Step 6

Multiply $3$ by $2$ .

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

Step 7

Multiply $- 5$ by $2$ .

$\frac{6 n^{3} - 10 m}{m}$

Step 8

Split the fraction $\frac{6 n^{3} - 10 m}{m}$ into two fractions.

$\frac{6 n^{3}}{m} + \frac{- 10 m}{m}$

Step 9

Cancel the common factor of $m$ .

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Step 9.1

Cancel the common factor.

$\frac{6 n^{3}}{m} + \frac{- 10 m}{m}$

Step 9.2

Divide $- 10$ by $1$ .

$\frac{6 n^{3}}{m} - 10$