Pre-Algebra Examples

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

Step 1

Combine $\frac{1}{2}$ and $y^{2}$ .

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

Step 2

Apply the distributive property.

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

Step 3

Simplify.

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Step 3.1

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

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Step 3.1.1

Move $x^{2}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Add $2$ and $2$ .

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Move the leading negative in $- \frac{x y}{6}$ into the numerator.

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

Step 3.2.2

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

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

Step 3.2.3

Factor $2$ out of $6$ .

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

Step 3.2.4

Cancel the common factor.

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

Step 3.2.5

Rewrite the expression.

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

Step 3.3

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

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

Step 3.4

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

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Step 3.4.1

Move $x$ .

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

Step 3.4.2

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

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Step 3.4.2.1

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

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

Step 3.4.2.2

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

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

Step 3.4.3

Add $1$ and $2$ .

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

Step 3.5

Combine $\frac{x^{3} (- 1 y)}{3}$ and $y$ .

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

Step 3.6

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

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

Step 3.7

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

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

Step 3.8

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

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

Step 3.9

Add $1$ and $1$ .

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

Step 3.10

Cancel the common factor of $2$ .

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Step 3.10.1

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

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

Step 3.10.2

Cancel the common factor.

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

Step 3.10.3

Rewrite the expression.

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

Step 3.11

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

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Step 3.11.1

Move $y^{2}$ .

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

Step 3.11.2

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

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Step 3.11.2.1

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

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

Step 3.11.2.2

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

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

Step 3.11.3

Add $2$ and $1$ .

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

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $- 2$ .

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

Step 4.2

Simplify the numerator.

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Step 4.2.1

Rewrite.

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

Step 4.2.2

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

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

Step 4.2.3

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

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

Step 4.2.4

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

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

Step 4.2.5

Add $1$ and $1$ .

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

Step 4.2.6

Remove unnecessary parentheses.

$- 8 x^{4} y - 1 \frac{x^{3} \cdot - 1 y^{2}}{3} - x^{2} y^{3}$

Step 4.2.7

Factor out negative.

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

Step 4.3

Move the negative in front of the fraction.

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

Step 4.4

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

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Step 4.4.1

Multiply $- 1$ by $- 1$ .

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

Step 4.4.2

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

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

Step 5

Simplify the expression.

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Step 5.1

Move $- 8 x^{4} y$ .

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

Step 5.2

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

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