a, $x^2+2x+1= x^2+2x.1+1^2= (x+1)^2$
b, $x^2-4x+4= x^2-2.x.2+2^2= (x-2)^2$
c, $4x^2-4x+1= (2x)^2-2.2x.1+1^2= (2x-1)^2$
d, $9x^2+6x+1= (3x)^2+2.3x.2+1^2= (3x+1)^2$
e, $x^2-x+\frac{1}{4}=x^2-2x.\frac{1}{2}+(\frac{1}{2})^2= (x-\frac{1}{2})^2$
f, $25x^2-10x+1= (5x)^2-2.5x.1+1^2= (5x-1)^2$