Pre-Algebra Examples

$(7 x y^{4} - 27 x^{5} y^{4}) \div (- 3 x^{4} y^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{7 x y^{4} - 27 x^{5} y^{4}}{- 3 x^{4} y^{3}}$

Step 2

Factor $x y^{4}$ out of $7 x y^{4} - 27 x^{5} y^{4}$ .

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Step 2.1

Factor $x y^{4}$ out of $7 x y^{4}$ .

$\frac{x y^{4} (7) - 27 x^{5} y^{4}}{- 3 x^{4} y^{3}}$

Step 2.2

Factor $x y^{4}$ out of $- 27 x^{5} y^{4}$ .

$\frac{x y^{4} (7) + x y^{4} (- 27 x^{4})}{- 3 x^{4} y^{3}}$

Step 2.3

Factor $x y^{4}$ out of $x y^{4} (7) + x y^{4} (- 27 x^{4})$ .

$\frac{x y^{4} (7 - 27 x^{4})}{- 3 x^{4} y^{3}}$

Step 3

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

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Step 3.1

Factor $x$ out of $x y^{4} (7 - 27 x^{4})$ .

$\frac{x (y^{4} (7 - 27 x^{4}))}{- 3 x^{4} y^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x (y^{4} (7 - 27 x^{4}))}{x (- 3 x^{3} y^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{x (y^{4} (7 - 27 x^{4}))}{x (- 3 x^{3} y^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{4} (7 - 27 x^{4})}{- 3 x^{3} y^{3}}$

Step 4

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

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Step 4.1

Factor $y^{3}$ out of $y^{4} (7 - 27 x^{4})$ .

$\frac{y^{3} (y (7 - 27 x^{4}))}{- 3 x^{3} y^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{y^{3} (y (7 - 27 x^{4}))}{y^{3} (- 3 x^{3})}$

Step 4.2.2

Cancel the common factor.

$\frac{y^{3} (y (7 - 27 x^{4}))}{y^{3} (- 3 x^{3})}$

Step 4.2.3

Rewrite the expression.

$\frac{y (7 - 27 x^{4})}{- 3 x^{3}}$

Step 5

Move the negative in front of the fraction.

$- \frac{y (7 - 27 x^{4})}{3 x^{3}}$

Step 6

Apply the distributive property.

$- \frac{y \cdot 7 + y (- 27 x^{4})}{3 x^{3}}$

Step 7

Move $7$ to the left of $y$ .

$- \frac{7 \cdot y + y (- 27 x^{4})}{3 x^{3}}$

Step 8

Rewrite using the commutative property of multiplication.

$- \frac{7 y - 27 y x^{4}}{3 x^{3}}$

Step 9

Split the fraction $\frac{7 y - 27 y x^{4}}{3 x^{3}}$ into two fractions.

$- (\frac{7 y}{3 x^{3}} + \frac{- 27 y x^{4}}{3 x^{3}})$

Step 10

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

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Step 10.1

Factor $3$ out of $- 27 y x^{4}$ .

$- (\frac{7 y}{3 x^{3}} + \frac{3 (- 9 y x^{4})}{3 x^{3}})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

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

$- (\frac{7 y}{3 x^{3}} + \frac{3 (- 9 y x^{4})}{3 (x^{3})})$

Step 10.2.2

Cancel the common factor.

$- (\frac{7 y}{3 x^{3}} + \frac{3 (- 9 y x^{4})}{3 x^{3}})$

Step 10.2.3

Rewrite the expression.

$- (\frac{7 y}{3 x^{3}} + \frac{- 9 y x^{4}}{x^{3}})$

Step 11

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

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Step 11.1

Factor $x^{3}$ out of $- 9 y x^{4}$ .

$- (\frac{7 y}{3 x^{3}} + \frac{x^{3} (- 9 y x)}{x^{3}})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Multiply by $1$ .

$- (\frac{7 y}{3 x^{3}} + \frac{x^{3} (- 9 y x)}{x^{3} \cdot 1})$

Step 11.2.2

Cancel the common factor.

$- (\frac{7 y}{3 x^{3}} + \frac{x^{3} (- 9 y x)}{x^{3} \cdot 1})$

Step 11.2.3

Rewrite the expression.

$- (\frac{7 y}{3 x^{3}} + \frac{- 9 y x}{1})$

Step 11.2.4

Divide $- 9 y x$ by $1$ .

$- (\frac{7 y}{3 x^{3}} - 9 y x)$