Pre-Algebra Examples

$(27 v^{6} z^{7} + 20 v^{6} z^{3} - 6 v z^{7}) \div (- 3 v^{4} z^{5})$

Step 1

Rewrite the division as a fraction.

$\frac{27 v^{6} z^{7} + 20 v^{6} z^{3} - 6 v z^{7}}{- 3 v^{4} z^{5}}$

Step 2

Factor $v z^{3}$ out of $27 v^{6} z^{7} + 20 v^{6} z^{3} - 6 v z^{7}$ .

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Step 2.1

Factor $v z^{3}$ out of $27 v^{6} z^{7}$ .

$\frac{v z^{3} (27 v^{5} z^{4}) + 20 v^{6} z^{3} - 6 v z^{7}}{- 3 v^{4} z^{5}}$

Step 2.2

Factor $v z^{3}$ out of $20 v^{6} z^{3}$ .

$\frac{v z^{3} (27 v^{5} z^{4}) + v z^{3} (20 v^{5}) - 6 v z^{7}}{- 3 v^{4} z^{5}}$

Step 2.3

Factor $v z^{3}$ out of $- 6 v z^{7}$ .

$\frac{v z^{3} (27 v^{5} z^{4}) + v z^{3} (20 v^{5}) + v z^{3} (- 6 z^{4})}{- 3 v^{4} z^{5}}$

Step 2.4

Factor $v z^{3}$ out of $v z^{3} (27 v^{5} z^{4}) + v z^{3} (20 v^{5})$ .

$\frac{v z^{3} (27 v^{5} z^{4} + 20 v^{5}) + v z^{3} (- 6 z^{4})}{- 3 v^{4} z^{5}}$

Step 2.5

Factor $v z^{3}$ out of $v z^{3} (27 v^{5} z^{4} + 20 v^{5}) + v z^{3} (- 6 z^{4})$ .

$\frac{v z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4})}{- 3 v^{4} z^{5}}$

Step 3

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

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Step 3.1

Factor $v$ out of $v z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4})$ .

$\frac{v (z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4}))}{- 3 v^{4} z^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $v$ out of $- 3 v^{4} z^{5}$ .

$\frac{v (z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4}))}{v (- 3 v^{3} z^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{v (z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4}))}{v (- 3 v^{3} z^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4})}{- 3 v^{3} z^{5}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $z^{3}$ out of $- 3 v^{3} z^{5}$ .

$\frac{z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4})}{z^{3} (- 3 v^{3} z^{2})}$

Step 4.2

Cancel the common factor.

$\frac{z^{3} (27 v^{5} z^{4} + 20 v^{5} - 6 z^{4})}{z^{3} (- 3 v^{3} z^{2})}$

Step 4.3

Rewrite the expression.

$\frac{27 v^{5} z^{4} + 20 v^{5} - 6 z^{4}}{- 3 v^{3} z^{2}}$

Step 5

Move the negative in front of the fraction.

$- \frac{27 v^{5} z^{4} + 20 v^{5} - 6 z^{4}}{3 v^{3} z^{2}}$

Step 6

Split the fraction $\frac{27 v^{5} z^{4} + 20 v^{5} - 6 z^{4}}{3 v^{3} z^{2}}$ into two fractions.

$- (\frac{27 v^{5} z^{4} + 20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 7

Split the fraction $\frac{27 v^{5} z^{4} + 20 v^{5}}{3 v^{3} z^{2}}$ into two fractions.

$- (\frac{27 v^{5} z^{4}}{3 v^{3} z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 8

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

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Step 8.1

Factor $3$ out of $27 v^{5} z^{4}$ .

$- (\frac{3 (9 v^{5} z^{4})}{3 v^{3} z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $3 v^{3} z^{2}$ .

$- (\frac{3 (9 v^{5} z^{4})}{3 (v^{3} z^{2})} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 8.2.2

Cancel the common factor.

$- (\frac{3 (9 v^{5} z^{4})}{3 (v^{3} z^{2})} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 8.2.3

Rewrite the expression.

$- (\frac{9 v^{5} z^{4}}{v^{3} z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 9

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

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Step 9.1

Factor $v^{3}$ out of $9 v^{5} z^{4}$ .

$- (\frac{v^{3} (9 v^{2} z^{4})}{v^{3} z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $v^{3}$ out of $v^{3} z^{2}$ .

$- (\frac{v^{3} (9 v^{2} z^{4})}{v^{3} (z^{2})} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 9.2.2

Cancel the common factor.

$- (\frac{v^{3} (9 v^{2} z^{4})}{v^{3} z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 9.2.3

Rewrite the expression.

$- (\frac{9 v^{2} z^{4}}{z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 10

Cancel the common factor of $z^{4}$ and $z^{2}$ .

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Step 10.1

Factor $z^{2}$ out of $9 v^{2} z^{4}$ .

$- (\frac{z^{2} (9 v^{2} z^{2})}{z^{2}} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Multiply by $1$ .

$- (\frac{z^{2} (9 v^{2} z^{2})}{z^{2} \cdot 1} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 10.2.2

Cancel the common factor.

$- (\frac{z^{2} (9 v^{2} z^{2})}{z^{2} \cdot 1} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 10.2.3

Rewrite the expression.

$- (\frac{9 v^{2} z^{2}}{1} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 10.2.4

Divide $9 v^{2} z^{2}$ by $1$ .

$- (9 v^{2} z^{2} + \frac{20 v^{5}}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 11

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

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Step 11.1

Factor $v^{3}$ out of $20 v^{5}$ .

$- (9 v^{2} z^{2} + \frac{v^{3} (20 v^{2})}{3 v^{3} z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $v^{3}$ out of $3 v^{3} z^{2}$ .

$- (9 v^{2} z^{2} + \frac{v^{3} (20 v^{2})}{v^{3} (3 z^{2})} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 11.2.2

Cancel the common factor.

$- (9 v^{2} z^{2} + \frac{v^{3} (20 v^{2})}{v^{3} (3 z^{2})} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 11.2.3

Rewrite the expression.

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{- 6 z^{4}}{3 v^{3} z^{2}})$

Step 12

Cancel the common factor of $- 6$ and $3$ .

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Step 12.1

Factor $3$ out of $- 6 z^{4}$ .

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{3 (- 2 z^{4})}{3 v^{3} z^{2}})$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $3$ out of $3 v^{3} z^{2}$ .

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{3 (- 2 z^{4})}{3 (v^{3} z^{2})})$

Step 12.2.2

Cancel the common factor.

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{3 (- 2 z^{4})}{3 (v^{3} z^{2})})$

Step 12.2.3

Rewrite the expression.

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{- 2 z^{4}}{v^{3} z^{2}})$

Step 13

Cancel the common factor of $z^{4}$ and $z^{2}$ .

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Step 13.1

Factor $z^{2}$ out of $- 2 z^{4}$ .

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{z^{2} (- 2 z^{2})}{v^{3} z^{2}})$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $z^{2}$ out of $v^{3} z^{2}$ .

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{z^{2} (- 2 z^{2})}{z^{2} v^{3}})$

Step 13.2.2

Cancel the common factor.

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{z^{2} (- 2 z^{2})}{z^{2} v^{3}})$

Step 13.2.3

Rewrite the expression.

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} + \frac{- 2 z^{2}}{v^{3}})$

Step 14

Move the negative in front of the fraction.

$- (9 v^{2} z^{2} + \frac{20 v^{2}}{3 z^{2}} - \frac{2 z^{2}}{v^{3}})$