Pre-Algebra Examples

$\frac{6 y^{7} x^{2} - 14 y^{7} x^{6}}{- 3 y^{5} x^{3}}$

Step 1

Factor $2 y^{7} x^{2}$ out of $6 y^{7} x^{2} - 14 y^{7} x^{6}$ .

Tap for more steps...

Step 1.1

Factor $2 y^{7} x^{2}$ out of $6 y^{7} x^{2}$ .

$\frac{2 y^{7} x^{2} (3) - 14 y^{7} x^{6}}{- 3 y^{5} x^{3}}$

Step 1.2

Factor $2 y^{7} x^{2}$ out of $- 14 y^{7} x^{6}$ .

$\frac{2 y^{7} x^{2} (3) + 2 y^{7} x^{2} (- 7 x^{4})}{- 3 y^{5} x^{3}}$

Step 1.3

Factor $2 y^{7} x^{2}$ out of $2 y^{7} x^{2} (3) + 2 y^{7} x^{2} (- 7 x^{4})$ .

$\frac{2 y^{7} x^{2} (3 - 7 x^{4})}{- 3 y^{5} x^{3}}$

Step 2

Cancel the common factor of $y^{7}$ and $y^{5}$ .

Tap for more steps...

Step 2.1

Factor $y^{5}$ out of $2 y^{7} x^{2} (3 - 7 x^{4})$ .

$\frac{y^{5} (2 y^{2} x^{2} (3 - 7 x^{4}))}{- 3 y^{5} x^{3}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $y^{5}$ out of $- 3 y^{5} x^{3}$ .

$\frac{y^{5} (2 y^{2} x^{2} (3 - 7 x^{4}))}{y^{5} (- 3 x^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{y^{5} (2 y^{2} x^{2} (3 - 7 x^{4}))}{y^{5} (- 3 x^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{2 y^{2} x^{2} (3 - 7 x^{4})}{- 3 x^{3}}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $x^{2}$ out of $2 y^{2} x^{2} (3 - 7 x^{4})$ .

$\frac{x^{2} (2 y^{2} (3 - 7 x^{4}))}{- 3 x^{3}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

$\frac{x^{2} (2 y^{2} (3 - 7 x^{4}))}{x^{2} (- 3 x)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (2 y^{2} (3 - 7 x^{4}))}{x^{2} (- 3 x)}$

Step 3.2.3

Rewrite the expression.

$\frac{2 y^{2} (3 - 7 x^{4})}{- 3 x}$

Step 4

Move the negative in front of the fraction.

$- \frac{2 y^{2} (3 - 7 x^{4})}{3 x}$

Step 5

Apply the distributive property.

$- \frac{2 y^{2} \cdot 3 + 2 y^{2} (- 7 x^{4})}{3 x}$

Step 6

Multiply $3$ by $2$ .

$- \frac{6 y^{2} + 2 y^{2} (- 7 x^{4})}{3 x}$

Step 7

Rewrite using the commutative property of multiplication.

$- \frac{6 y^{2} + 2 \cdot - 7 y^{2} x^{4}}{3 x}$

Step 8

Multiply $2$ by $- 7$ .

$- \frac{6 y^{2} - 14 y^{2} x^{4}}{3 x}$

Step 9

Split the fraction $\frac{6 y^{2} - 14 y^{2} x^{4}}{3 x}$ into two fractions.

$- (\frac{6 y^{2}}{3 x} + \frac{- 14 y^{2} x^{4}}{3 x})$

Step 10

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 10.1

Factor $3$ out of $6 y^{2}$ .

$- (\frac{3 (2 y^{2})}{3 x} + \frac{- 14 y^{2} x^{4}}{3 x})$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $3$ out of $3 x$ .

$- (\frac{3 (2 y^{2})}{3 (x)} + \frac{- 14 y^{2} x^{4}}{3 x})$

Step 10.2.2

Cancel the common factor.

$- (\frac{3 (2 y^{2})}{3 x} + \frac{- 14 y^{2} x^{4}}{3 x})$

Step 10.2.3

Rewrite the expression.

$- (\frac{2 y^{2}}{x} + \frac{- 14 y^{2} x^{4}}{3 x})$

Step 11

Cancel the common factor of $x^{4}$ and $x$ .

Tap for more steps...

Step 11.1

Factor $x$ out of $- 14 y^{2} x^{4}$ .

$- (\frac{2 y^{2}}{x} + \frac{x (- 14 y^{2} x^{3})}{3 x})$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $x$ out of $3 x$ .

$- (\frac{2 y^{2}}{x} + \frac{x (- 14 y^{2} x^{3})}{x \cdot 3})$

Step 11.2.2

Cancel the common factor.

$- (\frac{2 y^{2}}{x} + \frac{x (- 14 y^{2} x^{3})}{x \cdot 3})$

Step 11.2.3

Rewrite the expression.

$- (\frac{2 y^{2}}{x} + \frac{- 14 y^{2} x^{3}}{3})$

Step 12

Move the negative in front of the fraction.

$- (\frac{2 y^{2}}{x} - \frac{14 y^{2} x^{3}}{3})$