algebra question

Question

    x^2-y^2

----------------

  x^2-2xy+y^2

Answer 1

    x²-y²

--------------

x²-2xy+y²

 

Now x²-y² factors to (x+y)(x-y), and x²-2xy+y2 factors to (x-y)(x-y).  So:

 

     x²-y²            (x+y)(x-y)        (x+y)

-------------- =  ---------------  =  ---------,    for all x≠y

x²-2xy+y2        (x-y)(x-y)         (x-y)