How do you factor #64x^2-16x+1#?

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Answer 1 · 2015-05-05T10:01:49

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 = 64*1 = 64#
AND
#N_1 +N_2 = b = -16#

After trying out a few numbers we get #N_1 = -8# and #N_2 =-8#

#-8*-8 = 64#, and #(-8)+(-8)= -16#

#64x^2 - 16x + 1 = 64x^2 - 8x - 8x +1#

# = 8x(8x-1) - 1(8x - 1)#

#(8x - 1)# is a common factor to each of the terms

# = (8x-1)(8x-1) = color(green)((8x-1)^2#