SOLUTION: Is 4x^2-4x+1 a perfect square?

Algebra ->  Test -> SOLUTION: Is 4x^2-4x+1 a perfect square?      Log On


   

Question 452661: Is 4x^2-4x+1 a perfect square?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
to be a perfect square, it must fit this pattern:
A%5E2+%2B-+2AB+%2B+B%5E2
and it will equal %28A+%2B-+B%29%5E2 respectively for + or – sign in middle term.
4x%5E2+%96+4x+%2B+1 fits the pattern with A+=+2x and 2AB=-4x ..->.B=-4x%2F2A=-4x%2F2%2A2x=-4x%2F4x=-1 . .
so:
A%5E2+%2B-+2AB+%2B+B%5E2
%282x%29%5E2+-2%2A2x%28-1%29%2B%28-1%29%5E2+=%282x+%2B+1%29%5E2