Basic Math Examples

$a^{2} - 4 b^{2} + 5 a - 10 b$

Step 1

Regroup terms.

$a^{2} - 4 b^{2} + 5 a - 10 b$

Step 2

Rewrite $4 b^{2}$ as ${(2 b)}^{2}$ .

$a^{2} - {(2 b)}^{2} + 5 a - 10 b$

Step 3

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

$(a + 2 b) (a - (2 b)) + 5 a - 10 b$

Step 4

Multiply $2$ by $- 1$ .

$(a + 2 b) (a - 2 b) + 5 a - 10 b$

Step 5

Factor $5$ out of $5 a - 10 b$ .

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Step 5.1

Factor $5$ out of $5 a$ .

$(a + 2 b) (a - 2 b) + 5 (a) - 10 b$

Step 5.2

Factor $5$ out of $- 10 b$ .

$(a + 2 b) (a - 2 b) + 5 (a) + 5 (- 2 b)$

Step 5.3

Factor $5$ out of $5 (a) + 5 (- 2 b)$ .

$(a + 2 b) (a - 2 b) + 5 (a - 2 b)$

Step 6

Factor $a - 2 b$ out of $(a + 2 b) (a - 2 b) + 5 (a - 2 b)$ .

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Step 6.1

Factor $a - 2 b$ out of $(a + 2 b) (a - 2 b)$ .

$(a - 2 b) (a + 2 b) + 5 (a - 2 b)$

Step 6.2

Factor $a - 2 b$ out of $5 (a - 2 b)$ .

$(a - 2 b) (a + 2 b) + (a - 2 b) \cdot 5$

Step 6.3

Factor $a - 2 b$ out of $(a - 2 b) (a + 2 b) + (a - 2 b) \cdot 5$ .

$(a - 2 b) (a + 2 b + 5)$