How do you factor #16r^2 - 8r + 1#?

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Answer 1 · 2016-05-08T17:11:47

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

#16r^2 - 8r +1 #

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

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

#N_1*N_2 = a*c = 16* 1 = 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#

#16r^2 - 8r +1 = 16r^2 - 4r -4r+1 #

# 4r ( r - 1 ) - 1 ( 4r -1) #

#(r -1 )# is a common factor to each of the terms

# = (4r - 1 ) ( 4r - 1 ) #