Divide (20m^2n^3-10m^2n)/(5mn)

$\frac{20 m^{2} n^{3} - 10 m^{2} n}{5 m n}$

Step 1

Factor $10 m^{2} n$ out of $20 m^{2} n^{3} - 10 m^{2} n$ .

Factor $10 m^{2} n$ out of $20 m^{2} n^{3}$ .

$\frac{10 m^{2} n (2 n^{2}) - 10 m^{2} n}{5 m n}$

Factor $10 m^{2} n$ out of $- 10 m^{2} n$ .

$\frac{10 m^{2} n (2 n^{2}) + 10 m^{2} n (- 1)}{5 m n}$

Factor $10 m^{2} n$ out of $10 m^{2} n (2 n^{2}) + 10 m^{2} n (- 1)$ .

$\frac{10 m^{2} n (2 n^{2} - 1)}{5 m n}$

Step 2

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $10 m^{2} n (2 n^{2} - 1)$ .

$\frac{5 (2 m^{2} n (2 n^{2} - 1))}{5 m n}$

Cancel the common factors.

Factor $5$ out of $5 m n$ .

$\frac{5 (2 m^{2} n (2 n^{2} - 1))}{5 (m n)}$

Cancel the common factor.

$\frac{5 (2 m^{2} n (2 n^{2} - 1))}{5 (m n)}$

Rewrite the expression.

$\frac{2 m^{2} n (2 n^{2} - 1)}{m n}$

Step 3

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

Factor $m$ out of $2 m^{2} n (2 n^{2} - 1)$ .

$\frac{m (2 m n (2 n^{2} - 1))}{m n}$

Cancel the common factors.

Factor $m$ out of $m n$ .

$\frac{m (2 m n (2 n^{2} - 1))}{m (n)}$

Cancel the common factor.

$\frac{m (2 m n (2 n^{2} - 1))}{m n}$

Rewrite the expression.

$\frac{2 m n (2 n^{2} - 1)}{n}$

Step 4

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{2 m n (2 n^{2} - 1)}{n}$

Divide $2 m (2 n^{2} - 1)$ by $1$ .

$2 m (2 n^{2} - 1)$

Step 5

Apply the distributive property.

$2 m (2 n^{2}) + 2 m \cdot - 1$

Step 6

Rewrite using the commutative property of multiplication.

$2 \cdot 2 m n^{2} + 2 m \cdot - 1$

Step 7

Multiply $- 1$ by $2$ .

$2 \cdot 2 m n^{2} - 2 m$

Step 8

Multiply $2$ by $2$ .

$4 m n^{2} - 2 m$

Divide (20m^2n^3-10m^2n)/(5mn)

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