Basic Math Examples

$\frac{8 q^{2} r}{5 - p} \cdot \frac{3 (25 - p^{2})}{8 p q}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $25$ as $5^{2}$ .

$\frac{8 q^{2} r}{5 - p} \cdot \frac{3 (5^{2} - p^{2})}{8 p q}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5$ and $b = p$ .

$\frac{8 q^{2} r}{5 - p} \cdot \frac{3 (5 + p) (5 - p)}{8 p q}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $8 q$ .

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Step 2.1.1

Factor $8 q$ out of $8 q^{2} r$ .

$\frac{8 q (q r)}{5 - p} \cdot \frac{3 (5 + p) (5 - p)}{8 p q}$

Step 2.1.2

Factor $8 q$ out of $8 p q$ .

$\frac{8 q (q r)}{5 - p} \cdot \frac{3 (5 + p) (5 - p)}{8 q (p)}$

Step 2.1.3

Cancel the common factor.

$\frac{8 q (q r)}{5 - p} \cdot \frac{3 (5 + p) (5 - p)}{8 q p}$

Step 2.1.4

Rewrite the expression.

$\frac{q r}{5 - p} \cdot \frac{3 (5 + p) (5 - p)}{p}$

Step 2.2

Cancel the common factor of $5 - p$ .

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Step 2.2.1

Factor $5 - p$ out of $3 (5 + p) (5 - p)$ .

$\frac{q r}{5 - p} \cdot \frac{(5 - p) (3 (5 + p))}{p}$

Step 2.2.2

Cancel the common factor.

$\frac{q r}{5 - p} \cdot \frac{(5 - p) (3 (5 + p))}{p}$

Step 2.2.3

Rewrite the expression.

$q r \cdot \frac{3 (5 + p)}{p}$

Step 2.3

Combine $q$ and $\frac{3 (5 + p)}{p}$ .

$r \cdot \frac{q (3 (5 + p))}{p}$

Step 2.4

Combine $r$ and $\frac{q (3 (5 + p))}{p}$ .

$\frac{r (q (3 (5 + p)))}{p}$

Step 2.5

Move $3$ to the left of $r q$ .

$\frac{3 r q (5 + p)}{p}$