Algebra Examples

$\frac{15 x^{4} y^{2} - 30 x^{2} y^{3} + 45 x y}{5 x y}$

Step 1

Factor $15 x y$ out of $15 x^{4} y^{2} - 30 x^{2} y^{3} + 45 x y$ .

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Step 1.1

Factor $15 x y$ out of $15 x^{4} y^{2}$ .

$\frac{15 x y (x^{3} y) - 30 x^{2} y^{3} + 45 x y}{5 x y}$

Step 1.2

Factor $15 x y$ out of $- 30 x^{2} y^{3}$ .

$\frac{15 x y (x^{3} y) + 15 x y (- 2 x y^{2}) + 45 x y}{5 x y}$

Step 1.3

Factor $15 x y$ out of $45 x y$ .

$\frac{15 x y (x^{3} y) + 15 x y (- 2 x y^{2}) + 15 x y (3)}{5 x y}$

Step 1.4

Factor $15 x y$ out of $15 x y (x^{3} y) + 15 x y (- 2 x y^{2})$ .

$\frac{15 x y (x^{3} y - 2 x y^{2}) + 15 x y (3)}{5 x y}$

Step 1.5

Factor $15 x y$ out of $15 x y (x^{3} y - 2 x y^{2}) + 15 x y (3)$ .

$\frac{15 x y (x^{3} y - 2 x y^{2} + 3)}{5 x y}$

Step 2

Cancel the common factor of $15$ and $5$ .

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Step 2.1

Factor $5$ out of $15 x y (x^{3} y - 2 x y^{2} + 3)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $5 x y$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $y$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

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

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

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Multiply $- 2$ by $3$ .

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

Step 6.2

Multiply $3$ by $3$ .

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

$3 x^{3} y - 6 x y^{2} + 9$