Basic Math Examples

$\frac{p^{2} - q^{2}}{r + s} \cdot \frac{5 r + 5 s}{p - q}$

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

Factor $5$ out of $5 r + 5 s$ .

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Step 2.1.1

Factor $5$ out of $5 r$ .

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

Step 2.1.2

Factor $5$ out of $5 s$ .

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

Step 2.1.3

Factor $5$ out of $5 (r) + 5 (s)$ .

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

Step 2.2

Simplify terms.

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Step 2.2.1

Cancel the common factor of $p - q$ .

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Step 2.2.1.1

Factor $p - q$ out of $(p + q) (p - q)$ .

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

Step 2.2.1.2

Cancel the common factor.

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

Step 2.2.1.3

Rewrite the expression.

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

Step 2.2.2

Cancel the common factor of $r + s$ .

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Step 2.2.2.1

Factor $r + s$ out of $5 (r + s)$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

$(p + q) \cdot 5$

Step 2.2.3

Apply the distributive property.

$p \cdot 5 + q \cdot 5$

Step 2.2.4

Reorder.

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Step 2.2.4.1

Move $5$ to the left of $p$ .

$5 \cdot p + q \cdot 5$

Step 2.2.4.2

Move $5$ to the left of $q$ .

$5 \cdot p + 5 \cdot q$

Step 2.3

Multiply $5$ by $q$ .

$5 p + 5 q$