`a) x^3z+x^2yz−x^2z^2−xyz^2`
`=(x+y)(x^2.z−x.z^2)`
`=(x+y)(x−z)(xz)`
`b) x^3+x^2y−x^2z−xyz`
`=x^2(x+y)−xz(x+y)`
`=(x+y)(x^2−xz)`
`=(x+y).x.(x−z)`
`c) a^2x+a^2y+ax+ay+x+y`
`=a^2(x+y)+a(x+y)+(x+y)`
`=(x+y)(a^2+a+1)`
`d) a^2+2ab+b^2−c^2+2cd−d^2`
`=(a^2+2ab+b^2)−(c^2−2cd+d^2)`
`=(a+b)^2−(c−d)^2`
`=(a+b−c+d)(a+b+c−d)`