Algebra Examples

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

Step 1

Rewrite the division as a fraction.

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

Step 2

Factor $2 x^{2} y^{2}$ out of $2 x^{4} y^{2} - 4 x^{3} y^{3} + 6 x^{2} y^{4}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Factor $2 x^{2} y^{2}$ out of $6 x^{2} y^{4}$ .

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

Step 2.4

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

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

Step 2.5

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factors.

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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

Step 7

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

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

Step 8

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

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

Step 9

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

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Step 9.1

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

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $x$ out of $x y$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 10

Cancel the common factor of $x$ .

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Step 10.1

Cancel the common factor.

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

Step 10.2

Rewrite the expression.

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

Step 11

Cancel the common factor of $y$ .

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Step 11.1

Cancel the common factor.

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

Step 11.2

Divide $- 2$ by $1$ .

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

Step 12

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

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Step 12.1

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

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

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $y$ out of $x y$ .

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

Step 12.2.2

Cancel the common factor.

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

Step 12.2.3

Rewrite the expression.

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