Question

Factor 4x^2-4x+1 show all work please im trying to get this down.

Answer 1

ok this equation doesn't factor by the most basic of method, have you tried using complete the square, cause that would work

Answer 2

no how would you do that?
is there a way that works on all of them?

Answer 3

usually it will tell you how to do it
i'll show you the complete the square method if you'd like

Answer 4

is that definitely what the question says??

Answer 5

it says factor completly the it shows \[4x^2-4x+1\]

Answer 6

ok well firstly i'm gonna divide by 4 so there's no coefficient of x^2, this gives,
x^2-x+1/4 (you can see that this would equal (x-1/2)^2
(i can see an answer from here but i'd like to show you the complete the square method as it is used a lot later on)
Right, if you have a quadratic of the form x^2+bx+c, you can write it as;
(x+b/2)^2-((b/2)^2)+c, so in your case;

(x-1/2)^2-(-1/2)^2+1/4
(-1/2)^2 = 1/4
(x-1/2)^2+1/4-1/4
(x-1/2)^2 is your factorised equation