Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Combine $x$ and $\frac{1}{3}$ .

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

Step 1.2.2

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

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

Step 1.3

Combine $\frac{1}{6}$ and $y^{2}$ .

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

Step 2

Apply the distributive property.

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

Step 3

Simplify.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $6 x y$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

Move $x^{2}$ .

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

Step 3.2.2

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

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

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

Step 3.2.3

Add $2$ and $1$ .

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

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

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

Step 3.3.2

Factor $3$ out of $6 x y$ .

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

Step 3.3.3

Cancel the common factor.

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

Step 3.3.4

Rewrite the expression.

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

Step 3.4

Multiply $- 1$ by $2$ .

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

Step 3.5

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

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

Step 3.6

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

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

Step 3.7

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

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

Step 3.8

Add $1$ and $1$ .

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

Step 3.9

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

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

Step 3.10

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

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

Step 3.11

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

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

Step 3.12

Add $1$ and $1$ .

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

Step 3.13

Cancel the common factor of $6$ .

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Step 3.13.1

Factor $6$ out of $6 x y$ .

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

Step 3.13.2

Cancel the common factor.

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

Step 3.13.3

Rewrite the expression.

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

Step 3.14

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

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Step 3.14.1

Move $y^{2}$ .

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

Step 3.14.2

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

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Step 3.14.2.1

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

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

Step 3.14.2.2

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

$3 x^{3} y - 2 x^{2} y^{2} + x y^{2 + 1}$

Step 3.14.3

Add $2$ and $1$ .

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