How do you factor #4x^2+16x+16#?

1 Answer
Don't Memorise
May 17, 2015

#4x^2 + 16x + 16#

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 xxc = 4 xx 16 = 64#
and
#N_1 +N_2 = b = 16#

After trying out a few numbers we get #N_1 = 8# and #N_2 =8#
#8 xx 8 = 64#, and #8 +8= 16#

#4x^2 + 16x + 16 = 4x^2 + 8x +8x+ 16#
#= 4x (x + 2) +8 (x+2)#
#= (4x+8) (x + 2) #
The factor 4 is common to the terms in the first group above
# = {4(x+2)}(x+2)#
# =color(green)( {4(x+2)}(x+2))# is the Factorised form of #4x^2 + 16x + 16#

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