Solving binomials

Simplify 36x^2-24x+4
It shouldn't be simplify, it is already simple, it should be factorise.
At least, I am factorising (I think Americans spell it with a z)

=4(9x^2 - 6x + 1)

Now to factorise 9x^2 - 6x + 1
You need to look for two numbers that multiply to 9*1 = +9
and add to give -6

Since they multply to a positive number, the signs must both be the same
since they add to -6, the signs must both be negative

-3 x -3 = 9 and -3+-3=-6
so the numbers are -3 and -3
you have to replace -6x with -3x-3x

so
9x^2 - 6x + 1
=9x^2 - 3x - 3x + 1
now factorise in pairs
= 3x(3x-1) -1(3x-1) the brackets must be the same
= (3x - 1) (3x-1)

=(3x-1) ²
so
4(9x^2 - 6x + 1) = 4(3x-1) ²

I know this looks long winded but if you practice it on lots of examples it will become quite easy.

If you want me to explain some of my working better just ask me.

Thank you. That was the right answer.

But, I did this...is it also correct?

36x^2-24x+4

(6x-2)^2 because (6x-2)(6x-2)= is the same thing?

Yes it is the same but your answer is not fully factorised.

(6x-2)(6x-2)= 2(3x-1) * 2(3x-1) = 4(3x-1) ²