Algebra Examples

$\frac{15 m^{4} n^{3} - 35 m n^{2}}{5 m n}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Factor $5 m n^{2}$ out of $15 m^{4} n^{3} - 35 m n^{2}$ .

Tap for more steps...

Step 1.1.1

Factor $5 m n^{2}$ out of $15 m^{4} n^{3}$ .

$\frac{5 m n^{2} (3 m^{3} n) - 35 m n^{2}}{5 m n}$

Step 1.1.2

Factor $5 m n^{2}$ out of $- 35 m n^{2}$ .

$\frac{5 m n^{2} (3 m^{3} n) + 5 m n^{2} (- 7)}{5 m n}$

Step 1.1.3

Factor $5 m n^{2}$ out of $5 m n^{2} (3 m^{3} n) + 5 m n^{2} (- 7)$ .

$\frac{5 m n^{2} (3 m^{3} n - 7)}{5 m n}$

Step 1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\frac{5 m n^{2} (3 m^{3} n - 7)}{5 m n}$

Step 1.2.2

Rewrite the expression.

$\frac{m n^{2} (3 m^{3} n - 7)}{m n}$

Step 1.3

Cancel the common factor of $m$ .

Tap for more steps...

Step 1.3.1

Cancel the common factor.

$\frac{m n^{2} (3 m^{3} n - 7)}{m n}$

Step 1.3.2

Rewrite the expression.

$\frac{n^{2} (3 m^{3} n - 7)}{n}$

Step 1.4

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

Tap for more steps...

Step 1.4.1

Factor $n$ out of $n^{2} (3 m^{3} n - 7)$ .

$\frac{n (n (3 m^{3} n - 7))}{n}$

Step 1.4.2

Cancel the common factors.

Tap for more steps...

Step 1.4.2.1

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

$\frac{n (n (3 m^{3} n - 7))}{n^{1}}$

Step 1.4.2.2

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

$\frac{n (n (3 m^{3} n - 7))}{n \cdot 1}$

Step 1.4.2.3

Cancel the common factor.

$\frac{n (n (3 m^{3} n - 7))}{n \cdot 1}$

Step 1.4.2.4

Rewrite the expression.

$\frac{n (3 m^{3} n - 7)}{1}$

Step 1.4.2.5

Divide $n (3 m^{3} n - 7)$ by $1$ .

$n (3 m^{3} n - 7)$

Step 1.5

Apply the distributive property.

$n (3 m^{3} n) + n \cdot - 7$

Step 1.6

Reorder.

Tap for more steps...

Step 1.6.1

Rewrite using the commutative property of multiplication.

$3 n (m^{3} n) + n \cdot - 7$

Step 1.6.2

Move $- 7$ to the left of $n$ .

$3 n (m^{3} n) - 7 \cdot n$

Step 2

Multiply $n$ by $n$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $n$ .

$3 (n \cdot n) m^{3} - 7 \cdot n$

Step 2.2

Multiply $n$ by $n$ .

$3 n^{2} m^{3} - 7 \cdot n$

$3 n^{2} m^{3} - 7 n$