Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Factor $x^{2} y$ out of $x^{2} y (1) + x^{2} y (- x^{2} y^{3})$ .

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

Step 2

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

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Step 2.1

Factor $x$ out of $x^{2} y (1 - x^{2} y^{3})$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Cancel the common factor.

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

Step 2.2.4

Rewrite the expression.

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

Step 2.2.5

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

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $x$ by $1$ .

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $x^{2}$ .

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

Step 6.1.2

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

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Step 6.1.2.1

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

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

Step 6.1.2.2

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

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

Step 6.1.3

Add $2$ and $1$ .

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

Step 6.2

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

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Step 6.2.1

Move $y^{3}$ .

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

Step 6.2.2

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

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Step 6.2.2.1

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

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

Step 6.2.2.2

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

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

Step 6.2.3

Add $3$ and $1$ .

$x y - x^{3} y^{4}$