find the missing term: X^2 - 2x + __________ = (________) ^2

Question

algebra 2 find the missing term

Answer 1

X² - 2x + __________ = (________) ²

 

Start with the general formula:

    (a+b)(c+d) = ac + ad + bc + bd             [this is F-O-I-L]

 

Now, this is quite interesting in the case of:

    (x+a)(x+b) = x² + (b+a)x + ab             [different a and b than before]

  That means:

     b+a = -2

    and

     a=b      [because (x+a)=(x+b); it results in (..)²]

 

So,  a+b=-2

       b + b = -2          [substituting for a]

        2b = -2

          b = -1              [and also a=-1]

 

         ab = (-1)(-1)

         ab = 1

 

X² - 2x + 1 = (x - 1)²

Answer 2

 

 

x^2-2x+1=(x-1)(x-1)