could someone help me please?

Question

Factor the following.

x^2-2x+1

 

I tried to do it on my own and the only setup i can come up with is, (x-2) (x+1) but that doesn't make sense :(

Answer 1

Remember F-O-I-L (First-Outside-Inside-Last). 
 
When an expression like (ax+b)(cx+d) is expanded using the Distributive Property (twice) it is:
    (ax+b)(cx+d)
    ax(cx+d)  +  b(cx+d)
     acx²  +  axd   +   bcx   +   bd
       F          O           I            L
      acx²   + (ad+bc)x   + bd
 
 
"To factor" means to find the values that were multiplied to get the expression.  What factors produced:
     x²    -2x  +  1
We need to find the values of:  a,b,c,d
    ac = 1
    (ad+bc)= -2
    bc = 1
 
     For a perfect square:  (ax+b)(ax+b), this is  a²=1, 2ab=-2, b²=1.  So, a=1 and b=-1, right?  (x-1)²
 
PLZ try to learn the various methods for finding numbers that add to produce a value and multiply to produce another value.  Also, learn to use the Quadratic Formula.
       x² - 2x + 1 = 0
       Using the Quadratic Formula, the values of x that satisfy the equation are:   1 and 1   which means
                 (x - 1)(x - 1) = 0
 
So,  a=1, b=-1. c=1, d=-1
 
This is a perfect square (which is likely the topic you are currently studying.)
 
To check:  Apply F-O-I-L to  (x - 1)(x - 1):
      F        O        I        L
    x²       - x     - x     + 1
    x² -2x + 1             Check!