How do you factor #8n^2 - 8n +2#?

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Answer 1 · 2015-09-22T16:49:08

#=color(blue)((4n-2) ( 2n-1) # is the factorised form of the expression.

#8n^2 -8n +2#

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

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

#N_1*N_2 = a*c = 8*2 = 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#

#8n^2 -color(blue)(8n) +2 = 8n^2 color(blue)(-4n - 4n) +2#

#=4n( 2n-1) - 2 (2n -1)#

#color(blue)((4n-2) ( 2n-1) # is the factorised form of the expression.