Pre-Algebra Examples

$(- 28 x^{5} y + 14 x^{4 y} + 21 x^{3} y) \div (- 7 x^{3 y})$

Step 1

Rewrite the division as a fraction.

$\frac{- 28 x^{5} y + 14 x^{4 y} + 21 x^{3} y}{- 7 x^{3 y}}$

Step 2

Cancel the common factor of $- 28 x^{5} y + 14 x^{4 y} + 21 x^{3} y$ and $- 7$ .

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Step 2.1

Factor $7$ out of $- 28 x^{5} y$ .

$\frac{7 (- 4 x^{5} y) + 14 x^{4 y} + 21 x^{3} y}{- 7 x^{3 y}}$

Step 2.2

Factor $7$ out of $14 x^{4 y}$ .

$\frac{7 (- 4 x^{5} y) + 7 (2 x^{4 y}) + 21 x^{3} y}{- 7 x^{3 y}}$

Step 2.3

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

$\frac{7 (- 4 x^{5} y + 2 x^{4 y}) + 21 x^{3} y}{- 7 x^{3 y}}$

Step 2.4

Factor $7$ out of $21 x^{3} y$ .

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

Step 2.5

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

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

Step 2.6

Cancel the common factors.

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Step 2.6.1

Factor $7$ out of $- 7 x^{3 y}$ .

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

Step 2.6.2

Cancel the common factor.

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

Step 2.6.3

Rewrite the expression.

$\frac{- 4 x^{5} y + 2 x^{4 y} + 3 x^{3} y}{- x^{3 y}}$

Step 3

Move the negative in front of the fraction.

$- \frac{- 4 x^{5} y + 2 x^{4 y} + 3 x^{3} y}{x^{3 y}}$

Step 4

Factor $- 1$ out of $- 4 x^{5} y$ .

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

Step 5

Factor $- 1$ out of $2 x^{4 y}$ .

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

Step 6

Factor $- 1$ out of $- (4 x^{5} y) - (- 2 x^{4 y})$ .

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

Step 7

Factor $- 1$ out of $3 x^{3} y$ .

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

Step 8

Factor $- 1$ out of $- (4 x^{5} y - 2 x^{4 y}) - (- 3 x^{3} y)$ .

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

Step 9

Rewrite $- (4 x^{5} y - 2 x^{4 y} - 3 x^{3} y)$ as $- 1 (4 x^{5} y - 2 x^{4 y} - 3 x^{3} y)$ .

$- \frac{- 1 (4 x^{5} y - 2 x^{4 y} - 3 x^{3} y)}{x^{3 y}}$

Step 10

Move the negative in front of the fraction.

$- - \frac{4 x^{5} y - 2 x^{4 y} - 3 x^{3} y}{x^{3 y}}$

Step 11

Multiply $- 1$ by $- 1$ .

$1 \frac{4 x^{5} y - 2 x^{4 y} - 3 x^{3} y}{x^{3 y}}$

Step 12

Multiply $\frac{4 x^{5} y - 2 x^{4 y} - 3 x^{3} y}{x^{3 y}}$ by $1$ .

$\frac{4 x^{5} y - 2 x^{4 y} - 3 x^{3} y}{x^{3 y}}$

Step 13

Split the fraction $\frac{4 x^{5} y - 2 x^{4 y} - 3 x^{3} y}{x^{3 y}}$ into two fractions.

$\frac{4 x^{5} y - 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 14

Split the fraction $\frac{4 x^{5} y - 2 x^{4 y}}{x^{3 y}}$ into two fractions.

$\frac{4 x^{5} y}{x^{3 y}} + \frac{- 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 15

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

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Step 15.1

Factor $x^{3 y}$ out of $4 x^{5} y$ .

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

Step 15.2

Cancel the common factors.

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Step 15.2.1

Multiply by $1$ .

$\frac{x^{3 y} (4 x^{5 - 3 y} y)}{x^{3 y} \cdot 1} + \frac{- 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 15.2.2

Cancel the common factor.

$\frac{x^{3 y} (4 x^{5 - 3 y} y)}{x^{3 y} \cdot 1} + \frac{- 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 15.2.3

Rewrite the expression.

$\frac{4 x^{5 - 3 y} y}{1} + \frac{- 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 15.2.4

Divide $4 x^{5 - 3 y} y$ by $1$ .

$4 x^{5 - 3 y} y + \frac{- 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 16

Reorder factors in $4 x^{5 - 3 y} y$ .

$4 y x^{5 - 3 y} + \frac{- 2 x^{4 y}}{x^{3 y}} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 17

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

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Step 17.1

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

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

Step 17.2

Cancel the common factors.

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Step 17.2.1

Multiply by $1$ .

$4 y x^{5 - 3 y} + \frac{x^{3 y} (- 2 x^{y})}{x^{3 y} \cdot 1} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 17.2.2

Cancel the common factor.

$4 y x^{5 - 3 y} + \frac{x^{3 y} (- 2 x^{y})}{x^{3 y} \cdot 1} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 17.2.3

Rewrite the expression.

$4 y x^{5 - 3 y} + \frac{- 2 x^{y}}{1} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 17.2.4

Divide $- 2 x^{y}$ by $1$ .

$4 y x^{5 - 3 y} - 2 x^{y} + \frac{- 3 x^{3} y}{x^{3 y}}$

Step 18

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

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Step 18.1

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

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

Step 18.2

Cancel the common factors.

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Step 18.2.1

Multiply by $1$ .

$4 y x^{5 - 3 y} - 2 x^{y} + \frac{x^{3 y} (- 3 x^{3 - 3 y} y)}{x^{3 y} \cdot 1}$

Step 18.2.2

Cancel the common factor.

$4 y x^{5 - 3 y} - 2 x^{y} + \frac{x^{3 y} (- 3 x^{3 - 3 y} y)}{x^{3 y} \cdot 1}$

Step 18.2.3

Rewrite the expression.

$4 y x^{5 - 3 y} - 2 x^{y} + \frac{- 3 x^{3 - 3 y} y}{1}$

Step 18.2.4

Divide $- 3 x^{3 - 3 y} y$ by $1$ .

$4 y x^{5 - 3 y} - 2 x^{y} - 3 x^{3 - 3 y} y$

Step 19

Reorder factors in $- 3 x^{3 - 3 y} y$ .

$4 y x^{5 - 3 y} - 2 x^{y} - 3 y x^{3 - 3 y}$