Pre-Algebra Examples

$(- 24 x y^{5} + 6 x^{7} y^{5} + 21 x^{2} y^{3}) \div 3 x^{2} y^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{- 24 x y^{5} + 6 x^{7} y^{5} + 21 x^{2} y^{3}}{3 x^{2} y^{3}}$

Step 2

Factor $3 x y^{3}$ out of $- 24 x y^{5} + 6 x^{7} y^{5} + 21 x^{2} y^{3}$ .

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Step 2.1

Factor $3 x y^{3}$ out of $- 24 x y^{5}$ .

$\frac{3 x y^{3} (- 8 y^{2}) + 6 x^{7} y^{5} + 21 x^{2} y^{3}}{3 x^{2} y^{3}}$

Step 2.2

Factor $3 x y^{3}$ out of $6 x^{7} y^{5}$ .

$\frac{3 x y^{3} (- 8 y^{2}) + 3 x y^{3} (2 x^{6} y^{2}) + 21 x^{2} y^{3}}{3 x^{2} y^{3}}$

Step 2.3

Factor $3 x y^{3}$ out of $21 x^{2} y^{3}$ .

$\frac{3 x y^{3} (- 8 y^{2}) + 3 x y^{3} (2 x^{6} y^{2}) + 3 x y^{3} (7 x)}{3 x^{2} y^{3}}$

Step 2.4

Factor $3 x y^{3}$ out of $3 x y^{3} (- 8 y^{2}) + 3 x y^{3} (2 x^{6} y^{2})$ .

$\frac{3 x y^{3} (- 8 y^{2} + 2 x^{6} y^{2}) + 3 x y^{3} (7 x)}{3 x^{2} y^{3}}$

Step 2.5

Factor $3 x y^{3}$ out of $3 x y^{3} (- 8 y^{2} + 2 x^{6} y^{2}) + 3 x y^{3} (7 x)$ .

$\frac{3 x y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x)}{3 x^{2} y^{3}}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{3 x y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x)}{3 x^{2} y^{3}}$

Step 3.2

Rewrite the expression.

$\frac{x y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x)}{x^{2} y^{3}}$

Step 4

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

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Step 4.1

Factor $x$ out of $x y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x)$ .

$\frac{x (y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x))}{x^{2} y^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{x (y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x))}{x (x y^{3})}$

Step 4.2.2

Cancel the common factor.

$\frac{x (y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x))}{x (x y^{3})}$

Step 4.2.3

Rewrite the expression.

$\frac{y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x)}{x y^{3}}$

Step 5

Cancel the common factor of $y^{3}$ .

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Step 5.1

Cancel the common factor.

$\frac{y^{3} (- 8 y^{2} + 2 x^{6} y^{2} + 7 x)}{x y^{3}}$

Step 5.2

Rewrite the expression.

$\frac{- 8 y^{2} + 2 x^{6} y^{2} + 7 x}{x}$

Step 6

Factor $- 1$ out of $- 8 y^{2}$ .

$\frac{- (8 y^{2}) + 2 x^{6} y^{2} + 7 x}{x}$

Step 7

Factor $- 1$ out of $2 x^{6} y^{2}$ .

$\frac{- (8 y^{2}) - (- 2 x^{6} y^{2}) + 7 x}{x}$

Step 8

Factor $- 1$ out of $- (8 y^{2}) - (- 2 x^{6} y^{2})$ .

$\frac{- (8 y^{2} - 2 x^{6} y^{2}) + 7 x}{x}$

Step 9

Factor $- 1$ out of $7 x$ .

$\frac{- (8 y^{2} - 2 x^{6} y^{2}) - (- 7 x)}{x}$

Step 10

Factor $- 1$ out of $- (8 y^{2} - 2 x^{6} y^{2}) - (- 7 x)$ .

$\frac{- (8 y^{2} - 2 x^{6} y^{2} - 7 x)}{x}$

Step 11

Rewrite $- (8 y^{2} - 2 x^{6} y^{2} - 7 x)$ as $- 1 (8 y^{2} - 2 x^{6} y^{2} - 7 x)$ .

$\frac{- 1 (8 y^{2} - 2 x^{6} y^{2} - 7 x)}{x}$

Step 12

Move the negative in front of the fraction.

$- \frac{8 y^{2} - 2 x^{6} y^{2} - 7 x}{x}$

Step 13

Split the fraction $\frac{8 y^{2} - 2 x^{6} y^{2} - 7 x}{x}$ into two fractions.

$- (\frac{8 y^{2} - 2 x^{6} y^{2}}{x} + \frac{- 7 x}{x})$

Step 14

Split the fraction $\frac{8 y^{2} - 2 x^{6} y^{2}}{x}$ into two fractions.

$- (\frac{8 y^{2}}{x} + \frac{- 2 x^{6} y^{2}}{x} + \frac{- 7 x}{x})$

Step 15

Cancel the common factor of $x^{6}$ and $x$ .

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Step 15.1

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

$- (\frac{8 y^{2}}{x} + \frac{x (- 2 x^{5} y^{2})}{x} + \frac{- 7 x}{x})$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Raise $x$ to the power of $1$ .

$- (\frac{8 y^{2}}{x} + \frac{x (- 2 x^{5} y^{2})}{x^{1}} + \frac{- 7 x}{x})$

Step 15.2.2

Factor $x$ out of $x^{1}$ .

$- (\frac{8 y^{2}}{x} + \frac{x (- 2 x^{5} y^{2})}{x \cdot 1} + \frac{- 7 x}{x})$

Step 15.2.3

Cancel the common factor.

$- (\frac{8 y^{2}}{x} + \frac{x (- 2 x^{5} y^{2})}{x \cdot 1} + \frac{- 7 x}{x})$

Step 15.2.4

Rewrite the expression.

$- (\frac{8 y^{2}}{x} + \frac{- 2 x^{5} y^{2}}{1} + \frac{- 7 x}{x})$

Step 15.2.5

Divide $- 2 x^{5} y^{2}$ by $1$ .

$- (\frac{8 y^{2}}{x} - 2 x^{5} y^{2} + \frac{- 7 x}{x})$

Step 16

Cancel the common factor of $x$ .

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Step 16.1

Cancel the common factor.

$- (\frac{8 y^{2}}{x} - 2 x^{5} y^{2} + \frac{- 7 x}{x})$

Step 16.2

Divide $- 7$ by $1$ .

$- (\frac{8 y^{2}}{x} - 2 x^{5} y^{2} - 7)$