How do you write # x^2 + 8x + 16 # in factored form?

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Answer 1 · 2015-09-16T16:10:00

#color(blue)((x+4)(x+4)#

#x^2+8x+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*c = 4*4 =16#
and
#N_1 +N_2 = b = 8#

After trying out a few numbers we get #N_1 = 4# and #N_2 =4#
#4*4 = 16# and #4+4=8#

#x^2+8x+16=x^2+4x +4x+16#
#=x(x+4)+4(x+4)#

#color(blue)((x+4)(x+4)#