a)x4+2x2+1=(x2)2+2.x2.1+12=(x2+1)2
b) 4x2-12xy+9y2=(2x)2-2.2x.3y+(3y)2=(2x-3y)2
c) -x2-2xy-y2= -(x2+2xy+y2)=-(x+y)2
d) (x+y)2-2(x+y)+1= (x+y-1)2
e)x3-3x2+3x-1= (x3-1)+(-3x2+3x)=(x-1)(x2+x+1)-3x(x-1)
=(x-1)(x2-2x+1)=(x-1)3
g) x3+6x2+12x+8= (x+2)3
h) x3+1-x2-x= (x+1)(x2-x+1)-(x2+x)=(x+1)(x2-x+1)-x(x+1)
=(x+1)(x-1)2
k) (x+y)3-x3-y3= (x+y)3-(x3+y3)=(x+y)3-(x+y)(x2-xy+y2)
= (x+y)[(x+y)2-(x2-xy+y2)]
= 3xy(x+y)