Algebra Examples

${(2 x + 3)}^{2} - 12 x - 18$

Step 1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$4 u^{2} - 9$

Step 2

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

${(2 u)}^{2} - 9$

Step 3

Rewrite $9$ as $3^{2}$ .

${(2 u)}^{2} - 3^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 u$ and $b = 3$ .

$(2 u + 3) (2 u - 3)$

Step 5

Replace all occurrences of $u$ with $x$ .

$(2 x + 3) (2 x - 3)$