Basic Math Examples

$5 p + 5 q + p^{2} - q^{2}$

Step 1

Regroup terms.

$5 p + 5 q + p^{2} - q^{2}$

Step 2

Factor $5$ out of $5 p + 5 q$ .

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Step 2.1

Factor $5$ out of $5 p$ .

$5 (p) + 5 q + p^{2} - q^{2}$

Step 2.2

Factor $5$ out of $5 q$ .

$5 (p) + 5 (q) + p^{2} - q^{2}$

Step 2.3

Factor $5$ out of $5 (p) + 5 (q)$ .

$5 (p + q) + p^{2} - q^{2}$

Step 3

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 $b = q$ .

$5 (p + q) + (p + q) (p - q)$

Step 4

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

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Step 4.1

Factor $p + q$ out of $5 (p + q)$ .

$(p + q) \cdot 5 + (p + q) (p - q)$

Step 4.2

Factor $p + q$ out of $(p + q) \cdot 5 + (p + q) (p - q)$ .

$(p + q) (5 + p - q)$