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

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Answer 1 · 2015-05-04T07:35:28

Factoring by $color(blue)(GROUPING)$ :

$x^2 + 4x+ 4$ in general form is $ax^2 + bx + c$ :

here:
$color(red)(a)$ $=$ 1 (coefficient of $x^2$ )
$color(red)(b)$ $=$ 4(coefficient of $x$ )
$color(red)(c)$ $=$ 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:
$x^2 + 4x+ 4 = x^2 + 2x + 2x + 4$ (splitting middle term)

$= x(x+2) + 2(x +2)$ ( taking out common terms )
$= (x+2)(x+2)$

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