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

1 Answer
May 5, 2015

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