Algebra Examples

$\frac{6 x^{2} y^{4} - 12 x^{4} y^{2}}{3 x}$

Step 1

Factor $6 x^{2} y^{2}$ out of $6 x^{2} y^{4} - 12 x^{4} y^{2}$ .

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Step 1.1

Factor $6 x^{2} y^{2}$ out of $6 x^{2} y^{4}$ .

$\frac{6 x^{2} y^{2} (y^{2}) - 12 x^{4} y^{2}}{3 x}$

Step 1.2

Factor $6 x^{2} y^{2}$ out of $- 12 x^{4} y^{2}$ .

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

Step 1.3

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $3 x$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

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

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

Step 4

Apply the distributive property.

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

Step 5

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

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Step 5.1

Move $y^{2}$ .

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

Step 5.2

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

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

Step 5.3

Add $2$ and $2$ .

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

Step 6

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

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Step 6.1

Move $x^{2}$ .

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

Step 6.2

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

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Step 6.2.1

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

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

Step 6.2.2

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

$2 x y^{4} + 2 x^{2 + 1} y^{2} \cdot - 2$

Step 6.3

Add $2$ and $1$ .

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

Step 7

Multiply $- 2$ by $2$ .

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