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)#