# How do you factor x^2+4x+4?

May 4, 2015

Factoring by $\textcolor{b l u e}{G R O U P I N G}$ :

${x}^{2} + 4 x + 4$ in general form is $a {x}^{2} + b x + c$ :

here:
$\textcolor{red}{a}$ $=$ 1 (coefficient of ${x}^{2}$)
$\textcolor{red}{b}$ $=$ 4(coefficient of $x$)
$\textcolor{red}{c}$ $=$ 4 (constant term)

now: a $.$ c $=$ 4 (product of first and last term of the equation)

now, we need to find two factors of $a . c$ which need to add up to the middle term (which is b )

$a . c = 4.1$
$a . c = 2.2$ , here , 2+2 adds up to 4:

so we can factor as follows:
${x}^{2} + 4 x + 4 = {x}^{2} + 2 x + 2 x + 4$ (splitting middle term)

$= x \left(x + 2\right) + 2 \left(x + 2\right)$ ( taking out common terms )
$= \left(x + 2\right) \left(x + 2\right)$