Pre-Algebra Examples

$\frac{12 x^{2} y^{2} + 8 x y^{2} - 8 y^{2}}{2 x^{2} y}$

Step 1

Factor $4 y^{2}$ out of $12 x^{2} y^{2} + 8 x y^{2} - 8 y^{2}$ .

Tap for more steps...

Step 1.1

Factor $4 y^{2}$ out of $12 x^{2} y^{2}$ .

$\frac{4 y^{2} (3 x^{2}) + 8 x y^{2} - 8 y^{2}}{2 x^{2} y}$

Step 1.2

Factor $4 y^{2}$ out of $8 x y^{2}$ .

$\frac{4 y^{2} (3 x^{2}) + 4 y^{2} (2 x) - 8 y^{2}}{2 x^{2} y}$

Step 1.3

Factor $4 y^{2}$ out of $- 8 y^{2}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $4$ and $2$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Apply the distributive property.

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

Step 5

Simplify.

Tap for more steps...

Step 5.1

Rewrite using the commutative property of multiplication.

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

Step 5.2

Rewrite using the commutative property of multiplication.

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

Step 5.3

Multiply $- 2$ by $2$ .

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

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Multiply $2$ by $3$ .

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

Step 6.2

Multiply $2$ by $2$ .

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

Step 7

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

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

Step 8

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

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

Step 9

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

Tap for more steps...

Step 9.1

Cancel the common factor.

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

Step 9.2

Divide $6 y$ by $1$ .

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

Step 10

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

Tap for more steps...

Step 10.1

Factor $x$ out of $4 y x$ .

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

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

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

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 11

Move the negative in front of the fraction.

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