Basic Math Examples

$\frac{10 p^{2} q^{2}}{p - 4} \div \frac{5 p q^{2}}{{(p - 4)}^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 p^{2} q^{2}}{p - 4} \cdot \frac{{(p - 4)}^{2}}{5 p q^{2}}$

Step 2

Cancel the common factor of $5 p q^{2}$ .

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Step 2.1

Factor $5 p q^{2}$ out of $10 p^{2} q^{2}$ .

$\frac{5 p q^{2} (2 p)}{p - 4} \cdot \frac{{(p - 4)}^{2}}{5 p q^{2}}$

Step 2.2

Cancel the common factor.

$\frac{5 p q^{2} (2 p)}{p - 4} \cdot \frac{{(p - 4)}^{2}}{5 p q^{2}}$

Step 2.3

Rewrite the expression.

$\frac{2 p}{p - 4} {(p - 4)}^{2}$

Step 3

Cancel the common factor of $p - 4$ .

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Step 3.1

Factor $p - 4$ out of ${(p - 4)}^{2}$ .

$\frac{2 p}{p - 4} ((p - 4) (p - 4))$

Step 3.2

Cancel the common factor.

$\frac{2 p}{p - 4} ((p - 4) (p - 4))$

Step 3.3

Rewrite the expression.

$2 p (p - 4)$

Step 4

Apply the distributive property.

$2 p \cdot p + 2 p \cdot - 4$

Step 5

Multiply $p$ by $p$ by adding the exponents.

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Step 5.1

Move $p$ .

$2 (p \cdot p) + 2 p \cdot - 4$

Step 5.2

Multiply $p$ by $p$ .

$2 p^{2} + 2 p \cdot - 4$

Step 6

Multiply $- 4$ by $2$ .

$2 p^{2} - 8 p$