Algebra Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 2 \frac{1}{x^{3}} y (5 y x^{5} + 8 x y - 4 y^{2} x^{2})$

Step 2

Combine $- 2$ and $\frac{1}{x^{3}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

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

Step 5

Move $2$ to the left of $y$ .

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

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

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

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Step 7.1.1

Move the leading negative in $- \frac{2 y}{x^{3}}$ into the numerator.

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

Step 7.1.2

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

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

Step 7.1.3

Cancel the common factor.

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

Step 7.1.4

Rewrite the expression.

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

Step 7.2

Multiply $5$ by $- 2$ .

$- 10 y (y x^{2}) - \frac{2 y}{x^{3}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.3

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

$- 10 (y^{1} y) x^{2} - \frac{2 y}{x^{3}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.4

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

$- 10 (y^{1} y^{1}) x^{2} - \frac{2 y}{x^{3}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.5

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

$- 10 y^{1 + 1} x^{2} - \frac{2 y}{x^{3}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.6

Add $1$ and $1$ .

$- 10 y^{2} x^{2} - \frac{2 y}{x^{3}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.7

Cancel the common factor of $x$ .

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Step 7.7.1

Move the leading negative in $- \frac{2 y}{x^{3}}$ into the numerator.

$- 10 y^{2} x^{2} + \frac{- 2 y}{x^{3}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.7.2

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

$- 10 y^{2} x^{2} + \frac{- 2 y}{x \cdot x^{2}} (8 x y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.7.3

Factor $x$ out of $8 x y$ .

$- 10 y^{2} x^{2} + \frac{- 2 y}{x \cdot x^{2}} (x (8 y)) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.7.4

Cancel the common factor.

$- 10 y^{2} x^{2} + \frac{- 2 y}{x \cdot x^{2}} (x (8 y)) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.7.5

Rewrite the expression.

$- 10 y^{2} x^{2} + \frac{- 2 y}{x^{2}} (8 y) - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.8

Combine $8$ and $\frac{- 2 y}{x^{2}}$ .

$- 10 y^{2} x^{2} + \frac{8 (- 2 y)}{x^{2}} y - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.9

Multiply $- 2$ by $8$ .

$- 10 y^{2} x^{2} + \frac{- 16 y}{x^{2}} y - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.10

Combine $\frac{- 16 y}{x^{2}}$ and $y$ .

$- 10 y^{2} x^{2} + \frac{- 16 y \cdot y}{x^{2}} - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.11

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

$- 10 y^{2} x^{2} + \frac{- 16 (y^{1} y)}{x^{2}} - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.12

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

$- 10 y^{2} x^{2} + \frac{- 16 (y^{1} y^{1})}{x^{2}} - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.13

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

$- 10 y^{2} x^{2} + \frac{- 16 y^{1 + 1}}{x^{2}} - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.14

Add $1$ and $1$ .

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} - \frac{2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.15

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

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Step 7.15.1

Move the leading negative in $- \frac{2 y}{x^{3}}$ into the numerator.

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{- 2 y}{x^{3}} (- 4 y^{2} x^{2})$

Step 7.15.2

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

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{- 2 y}{x^{2} x} (- 4 y^{2} x^{2})$

Step 7.15.3

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

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{- 2 y}{x^{2} x} (x^{2} (- 4 y^{2}))$

Step 7.15.4

Cancel the common factor.

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{- 2 y}{x^{2} x} (x^{2} (- 4 y^{2}))$

Step 7.15.5

Rewrite the expression.

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{- 2 y}{x} (- 4 y^{2})$

Step 7.16

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

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{- 4 (- 2 y)}{x} y^{2}$

Step 7.17

Multiply $- 2$ by $- 4$ .

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{8 y}{x} y^{2}$

Step 7.18

Combine $\frac{8 y}{x}$ and $y^{2}$ .

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{8 y \cdot y^{2}}{x}$

Step 7.19

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

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Step 7.19.1

Move $y^{2}$ .

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{8 (y^{2} y)}{x}$

Step 7.19.2

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

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Step 7.19.2.1

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

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{8 (y^{2} y^{1})}{x}$

Step 7.19.2.2

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

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{8 y^{2 + 1}}{x}$

Step 7.19.3

Add $2$ and $1$ .

$- 10 y^{2} x^{2} + \frac{- 16 y^{2}}{x^{2}} + \frac{8 y^{3}}{x}$

Step 8

Move the negative in front of the fraction.

$- 10 y^{2} x^{2} - \frac{16 y^{2}}{x^{2}} + \frac{8 y^{3}}{x}$

Step 9

Move $y^{2}$ .

$- 10 x^{2} y^{2} - \frac{16 y^{2}}{x^{2}} + \frac{8 y^{3}}{x}$

Step 10

Move $- \frac{16 y^{2}}{x^{2}}$ .

$- 10 x^{2} y^{2} + \frac{8 y^{3}}{x} - \frac{16 y^{2}}{x^{2}}$