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

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Answer 1 · 2016-03-16T12:36:10

#color(green)( (x+2) (x+2)# is the factorised form of the expression.

#x^2 + 4x +4#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*4= 4#

AND

#N_1 +N_2 = b = 4#

After trying out a few numbers we get #N_1 = 2# and #N_2 =2#

#2*2 = 4#, and #2+ 2 = 4#

#x^2 + color(green)(4x) +4 = x^2 + color(green)(2x + 2x) +4 #

#= x (x+2) + 2 ( x +2 )#

#= (x+2) (x+2)#

#color(green)( (x+2) (x+2)# is the factorised form of the expression.