Pre-Algebra Examples

$(32 z^{6} x^{6} - 27 z^{6} x^{3}) \div (- 4 z^{5} x^{4})$

Step 1

Rewrite the division as a fraction.

$\frac{32 z^{6} x^{6} - 27 z^{6} x^{3}}{- 4 z^{5} x^{4}}$

Step 2

Factor $z^{6} x^{3}$ out of $32 z^{6} x^{6} - 27 z^{6} x^{3}$ .

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Step 2.1

Factor $z^{6} x^{3}$ out of $32 z^{6} x^{6}$ .

$\frac{z^{6} x^{3} (32 x^{3}) - 27 z^{6} x^{3}}{- 4 z^{5} x^{4}}$

Step 2.2

Factor $z^{6} x^{3}$ out of $- 27 z^{6} x^{3}$ .

$\frac{z^{6} x^{3} (32 x^{3}) + z^{6} x^{3} (- 27)}{- 4 z^{5} x^{4}}$

Step 2.3

Factor $z^{6} x^{3}$ out of $z^{6} x^{3} (32 x^{3}) + z^{6} x^{3} (- 27)$ .

$\frac{z^{6} x^{3} (32 x^{3} - 27)}{- 4 z^{5} x^{4}}$

Step 3

Cancel the common factor of $z^{6}$ and $z^{5}$ .

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Step 3.1

Factor $z^{5}$ out of $z^{6} x^{3} (32 x^{3} - 27)$ .

$\frac{z^{5} (z x^{3} (32 x^{3} - 27))}{- 4 z^{5} x^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{z^{5} (z x^{3} (32 x^{3} - 27))}{z^{5} (- 4 x^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{z^{5} (z x^{3} (32 x^{3} - 27))}{z^{5} (- 4 x^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{z x^{3} (32 x^{3} - 27)}{- 4 x^{4}}$

Step 4

Cancel the common factor of $x^{3}$ and $x^{4}$ .

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Step 4.1

Factor $x^{3}$ out of $z x^{3} (32 x^{3} - 27)$ .

$\frac{x^{3} (z (32 x^{3} - 27))}{- 4 x^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{x^{3} (z (32 x^{3} - 27))}{x^{3} (- 4 x)}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{3} (z (32 x^{3} - 27))}{x^{3} (- 4 x)}$

Step 4.2.3

Rewrite the expression.

$\frac{z (32 x^{3} - 27)}{- 4 x}$

Step 5

Move the negative in front of the fraction.

$- \frac{z (32 x^{3} - 27)}{4 x}$

Step 6

Apply the distributive property.

$- \frac{z (32 x^{3}) + z \cdot - 27}{4 x}$

Step 7

Rewrite using the commutative property of multiplication.

$- \frac{32 z x^{3} + z \cdot - 27}{4 x}$

Step 8

Move $- 27$ to the left of $z$ .

$- \frac{32 z x^{3} - 27 z}{4 x}$

Step 9

Split the fraction $\frac{32 z x^{3} - 27 z}{4 x}$ into two fractions.

$- (\frac{32 z x^{3}}{4 x} + \frac{- 27 z}{4 x})$

Step 10

Cancel the common factor of $32$ and $4$ .

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Step 10.1

Factor $4$ out of $32 z x^{3}$ .

$- (\frac{4 (8 z x^{3})}{4 x} + \frac{- 27 z}{4 x})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $4$ out of $4 x$ .

$- (\frac{4 (8 z x^{3})}{4 (x)} + \frac{- 27 z}{4 x})$

Step 10.2.2

Cancel the common factor.

$- (\frac{4 (8 z x^{3})}{4 x} + \frac{- 27 z}{4 x})$

Step 10.2.3

Rewrite the expression.

$- (\frac{8 z x^{3}}{x} + \frac{- 27 z}{4 x})$

Step 11

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

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Step 11.1

Factor $x$ out of $8 z x^{3}$ .

$- (\frac{x (8 z x^{2})}{x} + \frac{- 27 z}{4 x})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

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

$- (\frac{x (8 z x^{2})}{x^{1}} + \frac{- 27 z}{4 x})$

Step 11.2.2

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

$- (\frac{x (8 z x^{2})}{x \cdot 1} + \frac{- 27 z}{4 x})$

Step 11.2.3

Cancel the common factor.

$- (\frac{x (8 z x^{2})}{x \cdot 1} + \frac{- 27 z}{4 x})$

Step 11.2.4

Rewrite the expression.

$- (\frac{8 z x^{2}}{1} + \frac{- 27 z}{4 x})$

Step 11.2.5

Divide $8 z x^{2}$ by $1$ .

$- (8 z x^{2} + \frac{- 27 z}{4 x})$

Step 12

Move the negative in front of the fraction.

$- (8 z x^{2} - \frac{27 z}{4 x})$