Pre-Algebra Examples

$\frac{10 x^{2} y^{2} + 25 x y^{2} - 10 y^{2}}{5 x^{2} y}$

Step 1

Factor $5 y^{2}$ out of $10 x^{2} y^{2} + 25 x y^{2} - 10 y^{2}$ .

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Step 1.1

Factor $5 y^{2}$ out of $10 x^{2} y^{2}$ .

$\frac{5 y^{2} (2 x^{2}) + 25 x y^{2} - 10 y^{2}}{5 x^{2} y}$

Step 1.2

Factor $5 y^{2}$ out of $25 x y^{2}$ .

$\frac{5 y^{2} (2 x^{2}) + 5 y^{2} (5 x) - 10 y^{2}}{5 x^{2} y}$

Step 1.3

Factor $5 y^{2}$ out of $- 10 y^{2}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Apply the distributive property.

$\frac{y (2 x^{2}) + y (5 x) + y \cdot - 2}{x^{2}}$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{2 y x^{2} + y (5 x) + y \cdot - 2}{x^{2}}$

Step 5.2

Rewrite using the commutative property of multiplication.

$\frac{2 y x^{2} + 5 y x + y \cdot - 2}{x^{2}}$

Step 5.3

Move $- 2$ to the left of $y$ .

$\frac{2 y x^{2} + 5 y x - 2 \cdot y}{x^{2}}$

$\frac{2 y x^{2} + 5 y x - 2 y}{x^{2}}$

Step 6

Split the fraction $\frac{2 y x^{2} + 5 y x - 2 y}{x^{2}}$ into two fractions.

$\frac{2 y x^{2} + 5 y x}{x^{2}} + \frac{- 2 y}{x^{2}}$

Step 7

Split the fraction $\frac{2 y x^{2} + 5 y x}{x^{2}}$ into two fractions.

$\frac{2 y x^{2}}{x^{2}} + \frac{5 y x}{x^{2}} + \frac{- 2 y}{x^{2}}$

Step 8

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

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Step 8.1

Cancel the common factor.

$\frac{2 y x^{2}}{x^{2}} + \frac{5 y x}{x^{2}} + \frac{- 2 y}{x^{2}}$

Step 8.2

Divide $2 y$ by $1$ .

$2 y + \frac{5 y x}{x^{2}} + \frac{- 2 y}{x^{2}}$

Step 9

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

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Step 9.1

Factor $x$ out of $5 y x$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

$2 y + \frac{x (5 y)}{x \cdot x} + \frac{- 2 y}{x^{2}}$

Step 9.2.2

Cancel the common factor.

$2 y + \frac{x (5 y)}{x \cdot x} + \frac{- 2 y}{x^{2}}$

Step 9.2.3

Rewrite the expression.

$2 y + \frac{5 y}{x} + \frac{- 2 y}{x^{2}}$

Step 10

Move the negative in front of the fraction.

$2 y + \frac{5 y}{x} - \frac{2 y}{x^{2}}$