Algebra Examples

$\frac{3 x^{3} y^{4} - 9 x^{5} y^{6} + 6 x^{3} y^{3}}{6 x^{3} y^{2}}$

Step 1

Factor $3 x^{3} y^{3}$ out of $3 x^{3} y^{4} - 9 x^{5} y^{6} + 6 x^{3} y^{3}$ .

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Step 1.1

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

$\frac{3 x^{3} y^{3} (y) - 9 x^{5} y^{6} + 6 x^{3} y^{3}}{6 x^{3} y^{2}}$

Step 1.2

Factor $3 x^{3} y^{3}$ out of $- 9 x^{5} y^{6}$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $3$ and $6$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $6 x^{3} y^{2}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $y^{3}$ and $y^{2}$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Multiply $y$ by $y$ .

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

Step 6.2

Rewrite using the commutative property of multiplication.

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

Step 6.3

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

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

Step 7

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

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Step 7.1

Move $y^{3}$ .

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

Step 7.2

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

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Step 7.2.1

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

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

Step 7.2.2

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

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

Step 7.3

Add $3$ and $1$ .

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

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

Step 8

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

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

Step 9

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

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

Step 10

Move the negative in front of the fraction.

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

Step 11

Cancel the common factor of $2$ .

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Step 11.1

Cancel the common factor.

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

Step 11.2

Divide $y$ by $1$ .

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