Pre-Algebra Examples

$\frac{27 x^{3} y^{3} - 33 x y^{4} - x^{3} y}{3 x y}$

Step 1

Factor $x y$ out of $27 x^{3} y^{3} - 33 x y^{4} - x^{3} y$ .

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Step 1.1

Factor $x y$ out of $27 x^{3} y^{3}$ .

$\frac{x y (27 x^{2} y^{2}) - 33 x y^{4} - x^{3} y}{3 x y}$

Step 1.2

Factor $x y$ out of $- 33 x y^{4}$ .

$\frac{x y (27 x^{2} y^{2}) + x y (- 33 y^{3}) - x^{3} y}{3 x y}$

Step 1.3

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

$\frac{x y (27 x^{2} y^{2}) + x y (- 33 y^{3}) + x y (- x^{2})}{3 x y}$

Step 1.4

Factor $x y$ out of $x y (27 x^{2} y^{2}) + x y (- 33 y^{3})$ .

$\frac{x y (27 x^{2} y^{2} - 33 y^{3}) + x y (- x^{2})}{3 x y}$

Step 1.5

Factor $x y$ out of $x y (27 x^{2} y^{2} - 33 y^{3}) + x y (- x^{2})$ .

$\frac{x y (27 x^{2} y^{2} - 33 y^{3} - x^{2})}{3 x y}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Cancel the common factor.

$\frac{x y (27 x^{2} y^{2} - 33 y^{3} - x^{2})}{3 x y}$

Step 2.2

Rewrite the expression.

$\frac{y (27 x^{2} y^{2} - 33 y^{3} - x^{2})}{3 y}$

Step 3

Cancel the common factor of $y$ .

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Step 3.1

Cancel the common factor.

$\frac{y (27 x^{2} y^{2} - 33 y^{3} - x^{2})}{3 y}$

Step 3.2

Rewrite the expression.

$\frac{27 x^{2} y^{2} - 33 y^{3} - x^{2}}{3}$

Step 4

Split the fraction $\frac{27 x^{2} y^{2} - 33 y^{3} - x^{2}}{3}$ into two fractions.

$\frac{27 x^{2} y^{2} - 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 5

Split the fraction $\frac{27 x^{2} y^{2} - 33 y^{3}}{3}$ into two fractions.

$\frac{27 x^{2} y^{2}}{3} + \frac{- 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 6

Cancel the common factor of $27$ and $3$ .

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Step 6.1

Factor $3$ out of $27 x^{2} y^{2}$ .

$\frac{3 (9 x^{2} y^{2})}{3} + \frac{- 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $3$ .

$\frac{3 (9 x^{2} y^{2})}{3 (1)} + \frac{- 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (9 x^{2} y^{2})}{3 \cdot 1} + \frac{- 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 6.2.3

Rewrite the expression.

$\frac{9 x^{2} y^{2}}{1} + \frac{- 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 6.2.4

Divide $9 x^{2} y^{2}$ by $1$ .

$9 x^{2} y^{2} + \frac{- 33 y^{3}}{3} + \frac{- x^{2}}{3}$

Step 7

Cancel the common factor of $- 33$ and $3$ .

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Step 7.1

Factor $3$ out of $- 33 y^{3}$ .

$9 x^{2} y^{2} + \frac{3 (- 11 y^{3})}{3} + \frac{- x^{2}}{3}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3$ .

$9 x^{2} y^{2} + \frac{3 (- 11 y^{3})}{3 (1)} + \frac{- x^{2}}{3}$

Step 7.2.2

Cancel the common factor.

$9 x^{2} y^{2} + \frac{3 (- 11 y^{3})}{3 \cdot 1} + \frac{- x^{2}}{3}$

Step 7.2.3

Rewrite the expression.

$9 x^{2} y^{2} + \frac{- 11 y^{3}}{1} + \frac{- x^{2}}{3}$

Step 7.2.4

Divide $- 11 y^{3}$ by $1$ .

$9 x^{2} y^{2} - 11 y^{3} + \frac{- x^{2}}{3}$

Step 8

Move the negative in front of the fraction.

$9 x^{2} y^{2} - 11 y^{3} - \frac{x^{2}}{3}$