a, 1-2x+x^2 = x^2 - 2x.1 + 1^2= (x-1)^2
b, 4y+4+y^2 = y^2 + 2y.2+ 2^2 = (y+2)^2
c, 1/16+1/2x+x^2 = x^2 + 2.x.\(\frac{1}{4}\)+ (1/4)^2 = (x+1/4)^2
d, 36x^2+12xy+y^2 = (6x)^2 + 2.6x.y + y^2 = (6x+y)^2
a) \(1-2x+x^2=\left(1-x\right)^2=\left(x-1\right)^2\)
b) \(4y+4+y^2=y^2+4y+4=\left(y+2\right)^2\)
c) \(\frac{1}{16}+\frac{1}{2}x+x^2=\left(x+\frac{1}{4}\right)^2\)
d) \(36x^2+12xy+y^2=\left(6x+y\right)^2\)