a) x4 + 2x3 + 2x2 + 2x + 1
=[ (x2)2 + 2.x2.x + x2 ] + (x2 + 2.x.1 + 12)
=(x2 + x)2 + (x + 1)2
=[x(x + 1)]2 + (x + 1)2
=x2(x + 1)2 + (x + 1)2
=(x2 + 1)(x + 1)2
b) x2 - 2x - 4y2 - 4y
= [x2 - (2y)2] - 2(x - 2y)
= (x - 2y)(x + 2y) - 2(x - 2y)
= (x + 2y - 2)(x - 2y)