Pre-Algebra Examples

$(9 x^{6} y^{3} - 6 x^{2} y^{5}) \div (- 3 x y^{2})$

Step 1

Rewrite the division as a fraction.

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

Step 2

Factor $3 x^{2} y^{3}$ out of $9 x^{6} y^{3} - 6 x^{2} y^{5}$ .

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Step 2.1

Factor $3 x^{2} y^{3}$ out of $9 x^{6} y^{3}$ .

$\frac{3 x^{2} y^{3} (3 x^{4}) - 6 x^{2} y^{5}}{- 3 x y^{2}}$

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{3}$ and $y^{2}$ .

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Step 5.1

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

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

Step 5.2

Move the negative one from the denominator of $\frac{x y (3 x^{4} - 2 y^{2})}{- 1}$ .

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

Step 6

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

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

Step 7

Apply the distributive property.

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

Step 8

Rewrite using the commutative property of multiplication.

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

Step 9

Rewrite using the commutative property of multiplication.

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

Step 10

Simplify each term.

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Step 10.1

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 10.1.1

Move $x^{4}$ .

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

Step 10.1.2

Multiply $x^{4}$ by $x$ .

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Step 10.1.2.1

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

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

Step 10.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 10.1.3

Add $4$ and $1$ .

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

Step 10.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 10.2.1

Move $y^{2}$ .

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

Step 10.2.2

Multiply $y^{2}$ by $y$ .

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Step 10.2.2.1

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

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

Step 10.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- (3 x^{5} y - 2 x y^{2 + 1})$

Step 10.2.3

Add $2$ and $1$ .

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

Step 11

Apply the distributive property.

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

Step 12

Multiply $3$ by $- 1$ .

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

Step 13

Multiply $- 2$ by $- 1$ .

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

Step 14

Remove parentheses.

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