Pre-Algebra Examples

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

Step 1

Factor $6 x^{3}$ out of $6 x^{4} - 12 x^{3}$ .

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Step 1.1

Factor $6 x^{3}$ out of $6 x^{4}$ .

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

Step 1.2

Factor $6 x^{3}$ out of $- 12 x^{3}$ .

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

Step 1.3

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

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

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

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $3 x (x - 2)$ by $1$ .

$3 x (x - 2)$

$3 x (x - 2)$

$3 x (x - 2)$

Step 4

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2$

Step 5

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2$

Step 5.2

Multiply $x$ by $x$ .

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

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

Step 6

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$