(1)3(x-1)^3y-(1-x)^3z
=3(x-1)^3y+(x-1)^3z
=(x-1)^3(3y+z)
(2)(3m+2n)^2-(2m+3n)^2
=[(3m+2n)+(2m+3n)][(3m+2n)-(2m+3n)]
=(5m+5n)(m-n)
=5(m+n)(m-n)
(3)3a(b^2+9)^2-108ab^2
=3a[(b^2+9)^2-36b^2]
=3a(b^2+9+6b)(b^2+9-6b)
=3a(b+3)^2(b-3)^2
(4)x^4(a-2b)+x^2y^2(2b-a)
=(a-2b)(x^4-x^2y^2)
=(a-2b)(x^2+xy)(x^-xy)
=x^2(a-2b)(1+y)(1-y)
(5)16(a-b)^2-25(a+b)^2
=[4(a-b)+5(a+b)][4(a-b)-5(a+b)]
=(9a+b)(-a-9b)
=-(9a+b)(a+9b)