How to Factorise help!!!!!!!!!!!!

Question

4a^2-4a+1?

Answer 1

Given that      4a²-4a+1

Now solve the factors method

Look at the product of the first and last coefficients: (4)(1) =  4.

We want two factors of  4 whose sum middle coefficient of-4, and they are -2 and -2.

=  4a² -2a -2a +1

Take out common terms 2a , -1

= 2a(2a-1) -1(2a-1)

Take out common  factor (2a-1)

=(2a-1)(2a-1) 

There fore given (4a²-4a+1) factors (2a-1) (2a-1).

            (or)

Given that  (4a² -4a+1)

[(2a)²-2.2a.1+(1)²]

compare that equation with mathematical index formula (a² -2ab+b²) = (a-b)² 

a=2a  and b=1

(a-b)² =( 2a-1)²

(4a²-4a+1) factor  (2a-1)²