a) A = x3 - 2y3 - 3xy2
= x3 - 2y3 - 4xy2 + xy2
= (x3 - 4xy2) + (xy2 - 2y3)
= x(x2 - 4y2) + y2(x - 2y)
= x(x + 2y)(x - 2y) + y2(x - 2y)
= (x - 2y)[ x(x + 2y) + y2 ]
= (x - 2y)( x2 + 2xy + y2)
= (x - 2y)(x + y)2
b) B = x6 - x4 - 2x3 + 2x2
= (x6 - x4) - (2x3 + 2x2)
= x4(x2 - 1) - 2x2(x - 1)
= x4(x +1)(x - 1) - 2x2(x - 1)
= (x - 1)[ x4(x + 1) - 2x2)
= (x -1)( x5 + x4 - 2x2)
= (x -1)( x5 - x4 + 2x4 - 2x3 + 2x3 - 2x2)
= (x - 1)[(x5 - x4) + (2x4 - 2x3) + (2x3 - 2x2)]
= (x - 1)[ x4(x - 1) + 2x3(x - 1) + 2x2( x - 1)]
= (x - 1)(x - 1)(x4 + 2x3 + 2x2)
= (x - 1)2(x4 + 2x3 + 2x2)
= (x - 1)2[ x2( x2 + 2x + 2)]
= x2(x - 1)2(x2 + 2x +2)