Calculus Examples

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

Step 1

Regroup terms.

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

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 $b = b$ .

$(a + b) (a - b) + a x + b x$

Step 3

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

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Step 3.1

Factor $x$ out of $a x$ .

$(a + b) (a - b) + x a + b x$

Step 3.2

Factor $x$ out of $b x$ .

$(a + b) (a - b) + x a + x b$

Step 3.3

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

$(a + b) (a - b) + x (a + b)$

Step 4

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

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Step 4.1

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

$(a + b) (a - b) + (a + b) x$

Step 4.2

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

$(a + b) (a - b + x)$