Pre-Algebra Examples

$(21 u^{5} y^{7} - 7 u^{5} y) \div (- 3 u^{4} y^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{21 u^{5} y^{7} - 7 u^{5} y}{- 3 u^{4} y^{2}}$

Step 2

Factor $7 u^{5} y$ out of $21 u^{5} y^{7} - 7 u^{5} y$ .

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Step 2.1

Factor $7 u^{5} y$ out of $21 u^{5} y^{7}$ .

$\frac{7 u^{5} y (3 y^{6}) - 7 u^{5} y}{- 3 u^{4} y^{2}}$

Step 2.2

Factor $7 u^{5} y$ out of $- 7 u^{5} y$ .

$\frac{7 u^{5} y (3 y^{6}) + 7 u^{5} y (- 1)}{- 3 u^{4} y^{2}}$

Step 2.3

Factor $7 u^{5} y$ out of $7 u^{5} y (3 y^{6}) + 7 u^{5} y (- 1)$ .

$\frac{7 u^{5} y (3 y^{6} - 1)}{- 3 u^{4} y^{2}}$

Step 3

Cancel the common factor of $u^{5}$ and $u^{4}$ .

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Step 3.1

Factor $u^{4}$ out of $7 u^{5} y (3 y^{6} - 1)$ .

$\frac{u^{4} (7 u y (3 y^{6} - 1))}{- 3 u^{4} y^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{u^{4} (7 u y (3 y^{6} - 1))}{u^{4} (- 3 y^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{u^{4} (7 u y (3 y^{6} - 1))}{u^{4} (- 3 y^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{7 u y (3 y^{6} - 1)}{- 3 y^{2}}$

Step 4

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

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Step 4.1

Factor $y$ out of $7 u y (3 y^{6} - 1)$ .

$\frac{y (7 u (3 y^{6} - 1))}{- 3 y^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{y (7 u (3 y^{6} - 1))}{y (- 3 y)}$

Step 4.2.2

Cancel the common factor.

$\frac{y (7 u (3 y^{6} - 1))}{y (- 3 y)}$

Step 4.2.3

Rewrite the expression.

$\frac{7 u (3 y^{6} - 1)}{- 3 y}$

Step 5

Move the negative in front of the fraction.

$- \frac{7 u (3 y^{6} - 1)}{3 y}$

Step 6

Apply the distributive property.

$- \frac{7 u (3 y^{6}) + 7 u \cdot - 1}{3 y}$

Step 7

Rewrite using the commutative property of multiplication.

$- \frac{7 \cdot 3 u y^{6} + 7 u \cdot - 1}{3 y}$

Step 8

Multiply $- 1$ by $7$ .

$- \frac{7 \cdot 3 u y^{6} - 7 u}{3 y}$

Step 9

Multiply $7$ by $3$ .

$- \frac{21 u y^{6} - 7 u}{3 y}$

Step 10

Split the fraction $\frac{21 u y^{6} - 7 u}{3 y}$ into two fractions.

$- (\frac{21 u y^{6}}{3 y} + \frac{- 7 u}{3 y})$

Step 11

Cancel the common factor of $21$ and $3$ .

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Step 11.1

Factor $3$ out of $21 u y^{6}$ .

$- (\frac{3 (7 u y^{6})}{3 y} + \frac{- 7 u}{3 y})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $3 y$ .

$- (\frac{3 (7 u y^{6})}{3 (y)} + \frac{- 7 u}{3 y})$

Step 11.2.2

Cancel the common factor.

$- (\frac{3 (7 u y^{6})}{3 y} + \frac{- 7 u}{3 y})$

Step 11.2.3

Rewrite the expression.

$- (\frac{7 u y^{6}}{y} + \frac{- 7 u}{3 y})$

Step 12

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

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Step 12.1

Factor $y$ out of $7 u y^{6}$ .

$- (\frac{y (7 u y^{5})}{y} + \frac{- 7 u}{3 y})$

Step 12.2

Cancel the common factors.

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Step 12.2.1

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

$- (\frac{y (7 u y^{5})}{y^{1}} + \frac{- 7 u}{3 y})$

Step 12.2.2

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

$- (\frac{y (7 u y^{5})}{y \cdot 1} + \frac{- 7 u}{3 y})$

Step 12.2.3

Cancel the common factor.

$- (\frac{y (7 u y^{5})}{y \cdot 1} + \frac{- 7 u}{3 y})$

Step 12.2.4

Rewrite the expression.

$- (\frac{7 u y^{5}}{1} + \frac{- 7 u}{3 y})$

Step 12.2.5

Divide $7 u y^{5}$ by $1$ .

$- (7 u y^{5} + \frac{- 7 u}{3 y})$

Step 13

Move the negative in front of the fraction.

$- (7 u y^{5} - \frac{7 u}{3 y})$