a) (x+y+4)(x+y-4)
=[(x+y)+4][(x+y)-4]
= (x+y)^2-4^2
= x^2+2xy+y^2-16
b)(x-y+6)(x+y-6)
= [x-(y-6)][x+(y-6)]
= x^2-(y-6)^2
= x^2-y^2+12y-36
c)(y+2z-3)(y-2z-3)
= [(y-3)+2z][(y-3)-2z]
= (y-3)^2-4z^2
= y^2-6y+9-4z^2
d>(x+2y+3z).(2y+3z-x)
= [(2y+3z)+x][(2y+3z)-x]
= (2y+3z)^2-x^2
= 4y^2+12yz+9z^2-x^2