Algebra Examples

$(- x^{5} y^{5} - \frac{1}{4} x^{3} y^{2} + \frac{2}{3} x^{5} y - 6 x y^{3}) \div (- 3 x^{2} y^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{- x^{5} y^{5} - \frac{1}{4} \cdot (x^{3} y^{2}) + \frac{2}{3} \cdot (x^{5} y) - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $x y$ out of $- x^{5} y^{5} - \frac{1}{4} \cdot x^{3} y^{2} + \frac{2}{3} \cdot x^{5} y - 6 x y^{3}$ .

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Step 2.1.1

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

$\frac{x y (- x^{4} y^{4}) - \frac{1}{4} \cdot x^{3} y^{2} + \frac{2}{3} \cdot x^{5} y - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2.1.2

Factor $x y$ out of $- \frac{1}{4} \cdot x^{3} y^{2}$ .

$\frac{x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y) + \frac{2}{3} \cdot x^{5} y - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2.1.3

Factor $x y$ out of $\frac{2}{3} \cdot x^{5} y$ .

$\frac{x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4}) - 6 x y^{3}}{- 3 x^{2} y^{3}}$

Step 2.1.4

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

$\frac{x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.1.5

Factor $x y$ out of $x y (- x^{4} y^{4}) + x y (- \frac{1}{4} \cdot x^{2} y)$ .

$\frac{x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.1.6

Factor $x y$ out of $x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y) + x y (\frac{2}{3} \cdot x^{4})$ .

$\frac{x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y + \frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.1.7

Factor $x y$ out of $x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y + \frac{2}{3} \cdot x^{4}) + x y (- 6 y^{2})$ .

$\frac{x y (- x^{4} y^{4} - \frac{1}{4} \cdot x^{2} y + \frac{2}{3} \cdot x^{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.2

Combine exponents.

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Step 2.2.1

Combine $x^{2}$ and $\frac{1}{4}$ .

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

Step 2.2.2

Combine $y$ and $\frac{x^{2}}{4}$ .

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

Step 2.2.3

Combine $\frac{2}{3}$ and $x^{4}$ .

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

Step 2.3

To write $- x^{4} y^{4}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.4

Combine $- x^{4} y^{4}$ and $\frac{4}{4}$ .

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Simplify the numerator.

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Step 2.6.1

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

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Step 2.6.1.1

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

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

Step 2.6.1.2

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

$\frac{x y (\frac{x^{2} y (- x^{2} y^{3} \cdot 4) + x^{2} y (- 1)}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.6.1.3

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

$\frac{x y (\frac{x^{2} y (- x^{2} y^{3} \cdot 4 - 1)}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.6.2

Multiply $4$ by $- 1$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.7

To write $\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4} \cdot \frac{3}{3} + \frac{2 x^{4}}{3} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.8

To write $\frac{2 x^{4}}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1)}{4} \cdot \frac{3}{3} + \frac{2 x^{4}}{3} \cdot \frac{4}{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.9.1

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

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{4 \cdot 3} + \frac{2 x^{4}}{3} \cdot \frac{4}{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9.2

Multiply $4$ by $3$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{12} + \frac{2 x^{4}}{3} \cdot \frac{4}{4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9.3

Multiply $\frac{2 x^{4}}{3}$ by $\frac{4}{4}$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{12} + \frac{2 x^{4} \cdot 4}{3 \cdot 4} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.9.4

Multiply $3$ by $4$ .

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3}{12} + \frac{2 x^{4} \cdot 4}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.10

Combine the numerators over the common denominator.

$\frac{x y (\frac{x^{2} y (- 4 x^{2} y^{3} - 1) \cdot 3 + 2 x^{4} \cdot 4}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11

Simplify the numerator.

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Step 2.11.1

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

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Step 2.11.1.1

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

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3) + 2 x^{4} \cdot 4}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.1.2

Factor $x^{2}$ out of $2 x^{4} \cdot 4$ .

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3) + x^{2} (2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.1.3

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

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3} - 1)) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.2

Apply the distributive property.

$\frac{x y (\frac{x^{2} ((y (- 4 x^{2} y^{3}) + y \cdot - 1) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.3

Rewrite using the commutative property of multiplication.

$\frac{x y (\frac{x^{2} ((- 4 y (x^{2} y^{3}) + y \cdot - 1) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.4

Move $- 1$ to the left of $y$ .

$\frac{x y (\frac{x^{2} ((- 4 y (x^{2} y^{3}) - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5

Simplify each term.

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Step 2.11.5.1

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 2.11.5.1.1

Move $y^{3}$ .

$\frac{x y (\frac{x^{2} ((- 4 (y^{3} y) x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.1.2

Multiply $y^{3}$ by $y$ .

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Step 2.11.5.1.2.1

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

$\frac{x y (\frac{x^{2} ((- 4 (y^{3} y^{1}) x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.1.2.2

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

$\frac{x y (\frac{x^{2} ((- 4 y^{3 + 1} x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.1.3

Add $3$ and $1$ .

$\frac{x y (\frac{x^{2} ((- 4 y^{4} x^{2} - 1 \cdot y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.5.2

Rewrite $- 1 y$ as $- y$ .

$\frac{x y (\frac{x^{2} ((- 4 y^{4} x^{2} - y) \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.6

Apply the distributive property.

$\frac{x y (\frac{x^{2} (- 4 y^{4} x^{2} \cdot 3 - y \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.7

Multiply $3$ by $- 4$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - y \cdot 3 + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.8

Multiply $3$ by $- 1$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 2 x^{2} \cdot 4)}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.11.9

Multiply $4$ by $2$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2})}{12} - 6 y^{2})}{- 3 x^{2} y^{3}}$

Step 2.12

To write $- 6 y^{2}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2})}{12} - 6 y^{2} \cdot \frac{12}{12})}{- 3 x^{2} y^{3}}$

Step 2.13

Combine $- 6 y^{2}$ and $\frac{12}{12}$ .

$\frac{x y (\frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2})}{12} + \frac{- 6 y^{2} \cdot 12}{12})}{- 3 x^{2} y^{3}}$

Step 2.14

Combine the numerators over the common denominator.

$\frac{x y \frac{x^{2} (- 12 y^{4} x^{2} - 3 y + 8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15

Simplify the numerator.

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Step 2.15.1

Apply the distributive property.

$\frac{x y \frac{x^{2} (- 12 y^{4} x^{2}) + x^{2} (- 3 y) + x^{2} (8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.2

Simplify.

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Step 2.15.2.1

Rewrite using the commutative property of multiplication.

$\frac{x y \frac{- 12 x^{2} (y^{4} x^{2}) + x^{2} (- 3 y) + x^{2} (8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.2.2

Rewrite using the commutative property of multiplication.

$\frac{x y \frac{- 12 x^{2} (y^{4} x^{2}) - 3 x^{2} y + x^{2} (8 x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.2.3

Rewrite using the commutative property of multiplication.

$\frac{x y \frac{- 12 x^{2} (y^{4} x^{2}) - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3

Simplify each term.

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Step 2.15.3.1

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

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Step 2.15.3.1.1

Move $x^{2}$ .

$\frac{x y \frac{- 12 (x^{2} x^{2}) y^{4} - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.1.2

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

$\frac{x y \frac{- 12 x^{2 + 2} y^{4} - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.1.3

Add $2$ and $2$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{2} x^{2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.2

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

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Step 2.15.3.2.1

Move $x^{2}$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 (x^{2} x^{2}) - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.2.2

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

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{2 + 2} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.3.2.3

Add $2$ and $2$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 6 y^{2} \cdot 12}{12}}{- 3 x^{2} y^{3}}$

Step 2.15.4

Multiply $12$ by $- 6$ .

$\frac{x y \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{12}}{- 3 x^{2} y^{3}}$

Step 2.16

Combine exponents.

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Step 2.16.1

Combine $x$ and $\frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{12}$ .

$\frac{y \frac{x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12}}{- 3 x^{2} y^{3}}$

Step 2.16.2

Combine $y$ and $\frac{x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12}$ .

$\frac{\frac{y (x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}))}{12}}{- 3 x^{2} y^{3}}$

Step 2.17

Remove unnecessary parentheses.

$\frac{\frac{y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12}}{- 3 x^{2} y^{3}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})}{12} \cdot \frac{1}{- 3 x^{2} y^{3}}$

Step 4

Combine.

$\frac{y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1}{12 (- 3 x^{2} y^{3})}$

Step 5

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

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Step 5.1

Factor $y$ out of $y x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1$ .

$\frac{y ((x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1)}{12 (- 3 x^{2} y^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y$ out of $12 (- 3 x^{2} y^{3})$ .

$\frac{y ((x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1)}{y (12 (- 3 x^{2} y^{2}))}$

Step 5.2.2

Cancel the common factor.

$\frac{y ((x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1)}{y (12 (- 3 x^{2} y^{2}))}$

Step 5.2.3

Rewrite the expression.

$\frac{(x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1}{12 (- 3 x^{2} y^{2})}$

Step 6

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

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Step 6.1

Factor $x$ out of $(x (- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2})) \cdot 1$ .

$\frac{x ((- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1)}{12 (- 3 x^{2} y^{2})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $x$ out of $12 (- 3 x^{2} y^{2})$ .

$\frac{x ((- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1)}{x (12 (- 3 x y^{2}))}$

Step 6.2.2

Cancel the common factor.

$\frac{x ((- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1)}{x (12 (- 3 x y^{2}))}$

Step 6.2.3

Rewrite the expression.

$\frac{(- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}) \cdot 1}{12 (- 3 x y^{2})}$

Step 7

Multiply $- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}$ by $1$ .

$\frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{12 (- 3 x y^{2})}$

Step 8

Multiply $- 3$ by $12$ .

$\frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{- 36 (x y^{2})}$

Step 9

Move the negative in front of the fraction.

$- \frac{- 12 x^{4} y^{4} - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 10

Factor $- 1$ out of $- 12 x^{4} y^{4}$ .

$- \frac{- (12 x^{4} y^{4}) - 3 x^{2} y + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 11

Factor $- 1$ out of $- 3 x^{2} y$ .

$- \frac{- (12 x^{4} y^{4}) - (3 x^{2} y) + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 12

Factor $- 1$ out of $- (12 x^{4} y^{4}) - (3 x^{2} y)$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y) + 8 x^{4} - 72 y^{2}}{36 x y^{2}}$

Step 13

Factor $- 1$ out of $8 x^{4}$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y) - (- 8 x^{4}) - 72 y^{2}}{36 x y^{2}}$

Step 14

Factor $- 1$ out of $- (12 x^{4} y^{4} + 3 x^{2} y) - (- 8 x^{4})$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}) - 72 y^{2}}{36 x y^{2}}$

Step 15

Factor $- 1$ out of $- 72 y^{2}$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}) - (72 y^{2})}{36 x y^{2}}$

Step 16

Factor $- 1$ out of $- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}) - (72 y^{2})$ .

$- \frac{- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})}{36 x y^{2}}$

Step 17

Rewrite $- (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})$ as $- 1 (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})$ .

$- \frac{- 1 (12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2})}{36 x y^{2}}$

Step 18

Move the negative in front of the fraction.

$- - \frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$

Step 19

Multiply $- 1$ by $- 1$ .

$1 \frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$

Step 20

Multiply $\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$ by $1$ .

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$

Step 21

Split the fraction $\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4} + 72 y^{2}}{36 x y^{2}}$ into two fractions.

$\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 22

Split the fraction $\frac{12 x^{4} y^{4} + 3 x^{2} y - 8 x^{4}}{36 x y^{2}}$ into two fractions.

$\frac{12 x^{4} y^{4} + 3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 23

Split the fraction $\frac{12 x^{4} y^{4} + 3 x^{2} y}{36 x y^{2}}$ into two fractions.

$\frac{12 x^{4} y^{4}}{36 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24

Cancel the common factor of $12$ and $36$ .

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Step 24.1

Factor $12$ out of $12 x^{4} y^{4}$ .

$\frac{12 (x^{4} y^{4})}{36 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24.2

Cancel the common factors.

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Step 24.2.1

Factor $12$ out of $36 x y^{2}$ .

$\frac{12 (x^{4} y^{4})}{12 (3 x y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24.2.2

Cancel the common factor.

$\frac{12 (x^{4} y^{4})}{12 (3 x y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 24.2.3

Rewrite the expression.

$\frac{x^{4} y^{4}}{3 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25

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

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Step 25.1

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

$\frac{x (x^{3} y^{4})}{3 x y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25.2

Cancel the common factors.

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Step 25.2.1

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

$\frac{x (x^{3} y^{4})}{x (3 y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25.2.2

Cancel the common factor.

$\frac{x (x^{3} y^{4})}{x (3 y^{2})} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 25.2.3

Rewrite the expression.

$\frac{x^{3} y^{4}}{3 y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26

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

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Step 26.1

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

$\frac{y^{2} (x^{3} y^{2})}{3 y^{2}} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26.2

Cancel the common factors.

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Step 26.2.1

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

$\frac{y^{2} (x^{3} y^{2})}{y^{2} \cdot 3} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26.2.2

Cancel the common factor.

$\frac{y^{2} (x^{3} y^{2})}{y^{2} \cdot 3} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 26.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{3 x^{2} y}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27

Cancel the common factor of $3$ and $36$ .

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Step 27.1

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

$\frac{x^{3} y^{2}}{3} + \frac{3 (x^{2} y)}{36 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27.2

Cancel the common factors.

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Step 27.2.1

Factor $3$ out of $36 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{3 (x^{2} y)}{3 (12 x y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{3 (x^{2} y)}{3 (12 x y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 27.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x^{2} y}{12 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28

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

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Step 28.1

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

$\frac{x^{3} y^{2}}{3} + \frac{x (x y)}{12 x y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28.2

Cancel the common factors.

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Step 28.2.1

Factor $x$ out of $12 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x (x y)}{x (12 y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x (x y)}{x (12 y^{2})} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 28.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x y}{12 y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29

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

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Step 29.1

Factor $y$ out of $x y$ .

$\frac{x^{3} y^{2}}{3} + \frac{y x}{12 y^{2}} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29.2

Cancel the common factors.

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Step 29.2.1

Factor $y$ out of $12 y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{y x}{y (12 y)} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{y x}{y (12 y)} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 29.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{- 8 x^{4}}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30

Cancel the common factor of $- 8$ and $36$ .

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Step 30.1

Factor $4$ out of $- 8 x^{4}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{4 (- 2 x^{4})}{36 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30.2

Cancel the common factors.

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Step 30.2.1

Factor $4$ out of $36 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{4 (- 2 x^{4})}{4 (9 x y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{4 (- 2 x^{4})}{4 (9 x y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 30.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{- 2 x^{4}}{9 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31

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

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Step 31.1

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

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{x (- 2 x^{3})}{9 x y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31.2

Cancel the common factors.

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Step 31.2.1

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

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{x (- 2 x^{3})}{x (9 y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{x (- 2 x^{3})}{x (9 y^{2})} + \frac{72 y^{2}}{36 x y^{2}}$

Step 31.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} + \frac{- 2 x^{3}}{9 y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 32

Move the negative in front of the fraction.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{72 y^{2}}{36 x y^{2}}$

Step 33

Cancel the common factor of $72$ and $36$ .

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Step 33.1

Factor $36$ out of $72 y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{36 (2 y^{2})}{36 x y^{2}}$

Step 33.2

Cancel the common factors.

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Step 33.2.1

Factor $36$ out of $36 x y^{2}$ .

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{36 (2 y^{2})}{36 (x y^{2})}$

Step 33.2.2

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{36 (2 y^{2})}{36 (x y^{2})}$

Step 33.2.3

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{2 y^{2}}{x y^{2}}$

Step 34

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

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Step 34.1

Cancel the common factor.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{2 y^{2}}{x y^{2}}$

Step 34.2

Rewrite the expression.

$\frac{x^{3} y^{2}}{3} + \frac{x}{12 y} - \frac{2 x^{3}}{9 y^{2}} + \frac{2}{x}$