Algebra Examples

$\frac{10 x^{2} - 20 x}{40 x^{3} - 80 x^{2}} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 1

Factor $10 x$ out of $10 x^{2} - 20 x$ .

Tap for more steps...

Step 1.1

Factor $10 x$ out of $10 x^{2}$ .

$\frac{10 x (x) - 20 x}{40 x^{3} - 80 x^{2}} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 1.2

Factor $10 x$ out of $- 20 x$ .

$\frac{10 x (x) + 10 x (- 2)}{40 x^{3} - 80 x^{2}} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 1.3

Factor $10 x$ out of $10 x (x) + 10 x (- 2)$ .

$\frac{10 x (x - 2)}{40 x^{3} - 80 x^{2}} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 2

Factor $40 x^{2}$ out of $40 x^{3} - 80 x^{2}$ .

Tap for more steps...

Step 2.1

Factor $40 x^{2}$ out of $40 x^{3}$ .

$\frac{10 x (x - 2)}{40 x^{2} (x) - 80 x^{2}} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 2.2

Factor $40 x^{2}$ out of $- 80 x^{2}$ .

$\frac{10 x (x - 2)}{40 x^{2} (x) + 40 x^{2} (- 2)} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 2.3

Factor $40 x^{2}$ out of $40 x^{2} (x) + 40 x^{2} (- 2)$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{3} + 80 x^{2}}{6 x + 30}$

Step 3

Factor $16 x^{2}$ out of $16 x^{3} + 80 x^{2}$ .

Tap for more steps...

Step 3.1

Factor $16 x^{2}$ out of $16 x^{3}$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{2} (x) + 80 x^{2}}{6 x + 30}$

Step 3.2

Factor $16 x^{2}$ out of $80 x^{2}$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{2} (x) + 16 x^{2} (5)}{6 x + 30}$

Step 3.3

Factor $16 x^{2}$ out of $16 x^{2} (x) + 16 x^{2} (5)$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{2} (x + 5)}{6 x + 30}$

Step 4

Factor $6$ out of $6 x + 30$ .

Tap for more steps...

Step 4.1

Factor $6$ out of $6 x$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{2} (x + 5)}{6 (x) + 30}$

Step 4.2

Factor $6$ out of $30$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{2} (x + 5)}{6 x + 6 \cdot 5}$

Step 4.3

Factor $6$ out of $6 x + 6 \cdot 5$ .

$\frac{10 x (x - 2)}{40 x^{2} (x - 2)} \cdot \frac{16 x^{2} (x + 5)}{6 (x + 5)}$

Step 5

Combine.

$\frac{10 x (x - 2) (16 x^{2} (x + 5))}{40 x^{2} (x - 2) (6 (x + 5))}$

Step 6

Multiply $x$ by $x^{2}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $x^{2}$ .

$\frac{10 (x^{2} x) (x - 2) (16 (x + 5))}{40 x^{2} (x - 2) (6 (x + 5))}$

Step 6.2

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 6.2.1

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

$\frac{10 (x^{2} x^{1}) (x - 2) (16 (x + 5))}{40 x^{2} (x - 2) (6 (x + 5))}$

Step 6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 x^{2 + 1} (x - 2) (16 (x + 5))}{40 x^{2} (x - 2) (6 (x + 5))}$

Step 6.3

Add $2$ and $1$ .

$\frac{10 x^{3} (x - 2) (16 (x + 5))}{40 x^{2} (x - 2) (6 (x + 5))}$

Step 7

Cancel the common factor of $10$ and $40$ .

Tap for more steps...

Step 7.1

Factor $10$ out of $10 x^{3} (x - 2) (16 (x + 5))$ .

$\frac{10 ((x^{3} (x - 2)) (16 (x + 5)))}{40 x^{2} (x - 2) (6 (x + 5))}$

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $10$ out of $40 x^{2} (x - 2) (6 (x + 5))$ .

$\frac{10 ((x^{3} (x - 2)) (16 (x + 5)))}{10 (4 x^{2} (x - 2) (6 (x + 5)))}$

Step 7.2.2

Cancel the common factor.

$\frac{10 ((x^{3} (x - 2)) (16 (x + 5)))}{10 (4 x^{2} (x - 2) (6 (x + 5)))}$

Step 7.2.3

Rewrite the expression.

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

Step 8

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Tap for more steps...

Step 8.1

Factor $x^{2}$ out of $(x^{3} (x - 2)) (16 (x + 5))$ .

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

Step 8.2

Cancel the common factors.

Tap for more steps...

Step 8.2.1

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

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$\frac{(x (x - 2)) (16 (x + 5))}{(4 (x - 2)) (6 (x + 5))}$

Step 9

Cancel the common factor of $x - 2$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$\frac{x (x - 2) (16 (x + 5))}{4 (x - 2) (6 (x + 5))}$

Step 9.2

Rewrite the expression.

$\frac{(x) (16 (x + 5))}{(4) (6 (x + 5))}$

Step 10

Cancel the common factor of $16$ and $4$ .

Tap for more steps...

Step 10.1

Factor $4$ out of $(x) (16 (x + 5))$ .

$\frac{4 (x (4 (x + 5)))}{(4) (6 (x + 5))}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Cancel the common factor.

$\frac{4 (x (4 (x + 5)))}{4 (6 (x + 5))}$

Step 10.2.2

Rewrite the expression.

$\frac{x (4 (x + 5))}{6 (x + 5)}$

Step 11

Cancel the common factor of $4$ and $6$ .

Tap for more steps...

Step 11.1

Factor $2$ out of $x (4 (x + 5))$ .

$\frac{2 (x (2 (x + 5)))}{6 (x + 5)}$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $2$ out of $6 (x + 5)$ .

$\frac{2 (x (2 (x + 5)))}{2 (3 (x + 5))}$

Step 11.2.2

Cancel the common factor.

$\frac{2 (x (2 (x + 5)))}{2 (3 (x + 5))}$

Step 11.2.3

Rewrite the expression.

$\frac{x (2 (x + 5))}{3 (x + 5)}$

Step 12

Cancel the common factor of $x + 5$ .

Tap for more steps...

Step 12.1

Cancel the common factor.

$\frac{x (2 (x + 5))}{3 (x + 5)}$

Step 12.2

Rewrite the expression.

$\frac{x \cdot (2)}{3}$

Step 13

Move $2$ to the left of $x$ .

$\frac{2 x}{3}$