Pre-Algebra Examples

$a^{2} - b^{2} + 3 a + 3 b$

Step 1

Regroup terms.

$a^{2} - b^{2} + 3 a + 3 b$

Step 2

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

$(a + b) (a - b) + 3 a + 3 b$

Step 3

Factor $3$ out of $3 a + 3 b$ .

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Step 3.1

Factor $3$ out of $3 a$ .

$(a + b) (a - b) + 3 (a) + 3 b$

Step 3.2

Factor $3$ out of $3 b$ .

$(a + b) (a - b) + 3 (a) + 3 (b)$

Step 3.3

Factor $3$ out of $3 (a) + 3 (b)$ .

$(a + b) (a - b) + 3 (a + b)$

Step 4

Factor $a + b$ out of $(a + b) (a - b) + 3 (a + b)$ .

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Step 4.1

Factor $a + b$ out of $3 (a + b)$ .

$(a + b) (a - b) + (a + b) \cdot 3$

Step 4.2

Factor $a + b$ out of $(a + b) (a - b) + (a + b) \cdot 3$ .

$(a + b) (a - b + 3)$