Pre-Algebra Examples

$(- 9 u^{2} y^{7} + 6 u^{7} y^{7}) \div (- 2 u^{5} y^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{- 9 u^{2} y^{7} + 6 u^{7} y^{7}}{- 2 u^{5} y^{4}}$

Step 2

Factor $3 u^{2} y^{7}$ out of $- 9 u^{2} y^{7} + 6 u^{7} y^{7}$ .

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Step 2.1

Factor $3 u^{2} y^{7}$ out of $- 9 u^{2} y^{7}$ .

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

Step 2.2

Factor $3 u^{2} y^{7}$ out of $6 u^{7} y^{7}$ .

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

Step 2.3

Factor $3 u^{2} y^{7}$ out of $3 u^{2} y^{7} (- 3) + 3 u^{2} y^{7} (2 u^{5})$ .

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

Step 3

Cancel the common factor of $u^{2}$ and $u^{5}$ .

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Step 3.1

Factor $u^{2}$ out of $3 u^{2} y^{7} (- 3 + 2 u^{5})$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $u^{2}$ out of $- 2 u^{5} y^{4}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $y^{7}$ and $y^{4}$ .

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Step 4.1

Factor $y^{4}$ out of $3 y^{7} (- 3 + 2 u^{5})$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{3 y^{3} (- 3 + 2 u^{5})}{- 2 u^{3}}$

Step 5

Move the negative in front of the fraction.

$- \frac{3 y^{3} (- 3 + 2 u^{5})}{2 u^{3}}$

Step 6

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 7

Factor $- 1$ out of $2 u^{5}$ .

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

Step 8

Factor $- 1$ out of $- 1 (3) - (- 2 u^{5})$ .

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

Step 9

Move the negative in front of the fraction.

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

Step 10

Multiply $- 1$ by $- 1$ .

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

Step 11

Multiply $\frac{(3 y^{3}) (3 - 2 u^{5})}{2 u^{3}}$ by $1$ .

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

Step 12

Reorder factors in $\frac{(3 y^{3}) (3 - 2 u^{5})}{2 u^{3}}$ .

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

Step 13

Apply the distributive property.

$\frac{3 y^{3} \cdot 3 + 3 y^{3} (- 2 u^{5})}{2 u^{3}}$

Step 14

Multiply $3$ by $3$ .

$\frac{9 y^{3} + 3 y^{3} (- 2 u^{5})}{2 u^{3}}$

Step 15

Rewrite using the commutative property of multiplication.

$\frac{9 y^{3} + 3 \cdot - 2 y^{3} u^{5}}{2 u^{3}}$

Step 16

Multiply $3$ by $- 2$ .

$\frac{9 y^{3} - 6 y^{3} u^{5}}{2 u^{3}}$

Step 17

Split the fraction $\frac{9 y^{3} - 6 y^{3} u^{5}}{2 u^{3}}$ into two fractions.

$\frac{9 y^{3}}{2 u^{3}} + \frac{- 6 y^{3} u^{5}}{2 u^{3}}$

Step 18

Cancel the common factor of $- 6$ and $2$ .

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Step 18.1

Factor $2$ out of $- 6 y^{3} u^{5}$ .

$\frac{9 y^{3}}{2 u^{3}} + \frac{2 (- 3 y^{3} u^{5})}{2 u^{3}}$

Step 18.2

Cancel the common factors.

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Step 18.2.1

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

$\frac{9 y^{3}}{2 u^{3}} + \frac{2 (- 3 y^{3} u^{5})}{2 (u^{3})}$

Step 18.2.2

Cancel the common factor.

$\frac{9 y^{3}}{2 u^{3}} + \frac{2 (- 3 y^{3} u^{5})}{2 u^{3}}$

Step 18.2.3

Rewrite the expression.

$\frac{9 y^{3}}{2 u^{3}} + \frac{- 3 y^{3} u^{5}}{u^{3}}$

Step 19

Cancel the common factor of $u^{5}$ and $u^{3}$ .

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Step 19.1

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

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

Step 19.2

Cancel the common factors.

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Step 19.2.1

Multiply by $1$ .

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

Step 19.2.2

Cancel the common factor.

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

Step 19.2.3

Rewrite the expression.

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

Step 19.2.4

Divide $- 3 y^{3} u^{2}$ by $1$ .

$\frac{9 y^{3}}{2 u^{3}} - 3 y^{3} u^{2}$