Algebra Examples

$\frac{16 x^{3} y^{6} - 24 x^{5} y^{5}}{- 4 x^{4} y^{3}}$

Step 1

Factor $8 x^{3} y^{5}$ out of $16 x^{3} y^{6} - 24 x^{5} y^{5}$ .

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Step 1.1

Factor $8 x^{3} y^{5}$ out of $16 x^{3} y^{6}$ .

$\frac{8 x^{3} y^{5} (2 y) - 24 x^{5} y^{5}}{- 4 x^{4} y^{3}}$

Step 1.2

Factor $8 x^{3} y^{5}$ out of $- 24 x^{5} y^{5}$ .

$\frac{8 x^{3} y^{5} (2 y) + 8 x^{3} y^{5} (- 3 x^{2})}{- 4 x^{4} y^{3}}$

Step 1.3

Factor $8 x^{3} y^{5}$ out of $8 x^{3} y^{5} (2 y) + 8 x^{3} y^{5} (- 3 x^{2})$ .

$\frac{8 x^{3} y^{5} (2 y - 3 x^{2})}{- 4 x^{4} y^{3}}$

Step 2

Cancel the common factor of $8$ and $- 4$ .

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Step 2.1

Factor $4$ out of $8 x^{3} y^{5} (2 y - 3 x^{2})$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Move the negative in front of the fraction.

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

Step 6

Apply the distributive property.

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

Step 7

Rewrite using the commutative property of multiplication.

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

Step 8

Rewrite using the commutative property of multiplication.

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

Step 9

Simplify each term.

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Step 9.1

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

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Step 9.1.1

Move $y$ .

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

Step 9.1.2

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

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Step 9.1.2.1

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

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

Step 9.1.2.2

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

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

Step 9.1.3

Add $1$ and $2$ .

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

Step 9.2

Multiply $2$ by $2$ .

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

Step 9.3

Multiply $2$ by $- 3$ .

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

Step 10

Split the fraction $\frac{4 y^{3} - 6 y^{2} x^{2}}{x}$ into two fractions.

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

Step 11

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

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Step 11.1

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

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

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

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

Step 11.2.2

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

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

Step 11.2.3

Cancel the common factor.

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

Step 11.2.4

Rewrite the expression.

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

Step 11.2.5

Divide $- 6 y^{2} x$ by $1$ .

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