Algebra Examples

$\frac{18 x^{3} y^{2} + 9 x^{2} y^{3} - 12 x^{3} y^{3} + 6 x y^{2}}{3 x y}$

Step 1

Factor $3 x y^{2}$ out of $18 x^{3} y^{2} + 9 x^{2} y^{3} - 12 x^{3} y^{3} + 6 x y^{2}$ .

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Step 1.1

Factor $3 x y^{2}$ out of $18 x^{3} y^{2}$ .

$\frac{3 x y^{2} (6 x^{2}) + 9 x^{2} y^{3} - 12 x^{3} y^{3} + 6 x y^{2}}{3 x y}$

Step 1.2

Factor $3 x y^{2}$ out of $9 x^{2} y^{3}$ .

$\frac{3 x y^{2} (6 x^{2}) + 3 x y^{2} (3 x y) - 12 x^{3} y^{3} + 6 x y^{2}}{3 x y}$

Step 1.3

Factor $3 x y^{2}$ out of $- 12 x^{3} y^{3}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

Factor $3 x y^{2}$ out of $3 x y^{2} (6 x^{2} + 3 x y) + 3 x y^{2} (- 4 x^{2} y)$ .

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

Step 1.7

Factor $3 x y^{2}$ out of $3 x y^{2} (6 x^{2} + 3 x y - 4 x^{2} y) + 3 x y^{2} (2)$ .

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

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $y$ out of $y^{2} (6 x^{2} + 3 x y - 4 x^{2} y + 2)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

Divide $y (6 x^{2} + 3 x y - 4 x^{2} y + 2)$ by $1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

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

Step 6.2

Rewrite using the commutative property of multiplication.

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

Step 6.3

Rewrite using the commutative property of multiplication.

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

Step 6.4

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

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

Step 7

Simplify each term.

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Step 7.1

Multiply $y$ by $y$ by adding the exponents.

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Step 7.1.1

Move $y$ .

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

Step 7.1.2

Multiply $y$ by $y$ .

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

Step 7.2

Multiply $y$ by $y$ by adding the exponents.

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Step 7.2.1

Move $y$ .

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

Step 7.2.2

Multiply $y$ by $y$ .

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

$6 y x^{2} + 3 y^{2} x - 4 y^{2} x^{2} + 2 y$