Question 452661
to be a perfect square, it must fit this pattern:

{{{A^2 +- 2AB + B^2}}}

and it will equal {{{(A +- B)^2}}} respectively for + or – sign in middle term.

{{{4x^2 – 4x + 1}}} fits the pattern with {{{A = 2x}}} and {{{2AB=-4x}}} ..->.{{{B=-4x/2A=-4x/2*2x=-4x/4x=-1}}} . .

so: 

{{{A^2 +- 2AB + B^2}}}

{{{(2x)^2 -2*2x(-1)+(-1)^2 =(2x + 1)^2}}}