Pre-Algebra Examples

$\frac{4 x^{3} + 16 x y + x^{2} y^{2}}{4 x y}$

Step 1

Factor $x$ out of $4 x^{3} + 16 x y + x^{2} y^{2}$ .

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Step 1.1

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

$\frac{x (4 x^{2}) + 16 x y + x^{2} y^{2}}{4 x y}$

Step 1.2

Factor $x$ out of $16 x y$ .

$\frac{x (4 x^{2}) + x (16 y) + x^{2} y^{2}}{4 x y}$

Step 1.3

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

$\frac{x (4 x^{2}) + x (16 y) + x (x y^{2})}{4 x y}$

Step 1.4

Factor $x$ out of $x (4 x^{2}) + x (16 y)$ .

$\frac{x (4 x^{2} + 16 y) + x (x y^{2})}{4 x y}$

Step 1.5

Factor $x$ out of $x (4 x^{2} + 16 y) + x (x y^{2})$ .

$\frac{x (4 x^{2} + 16 y + x y^{2})}{4 x y}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Cancel the common factor.

$\frac{x (4 x^{2} + 16 y + x y^{2})}{4 x y}$

Step 2.2

Rewrite the expression.

$\frac{4 x^{2} + 16 y + x y^{2}}{4 y}$

Step 3

Split the fraction $\frac{4 x^{2} + 16 y + x y^{2}}{4 y}$ into two fractions.

$\frac{4 x^{2} + 16 y}{4 y} + \frac{x y^{2}}{4 y}$

Step 4

Split the fraction $\frac{4 x^{2} + 16 y}{4 y}$ into two fractions.

$\frac{4 x^{2}}{4 y} + \frac{16 y}{4 y} + \frac{x y^{2}}{4 y}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Cancel the common factor.

$\frac{4 x^{2}}{4 y} + \frac{16 y}{4 y} + \frac{x y^{2}}{4 y}$

Step 5.2

Rewrite the expression.

$\frac{x^{2}}{y} + \frac{16 y}{4 y} + \frac{x y^{2}}{4 y}$

Step 6

Cancel the common factor of $16$ and $4$ .

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Step 6.1

Factor $4$ out of $16 y$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $y$ out of $4 y$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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