Factorization of x^6+63x^3-64

Solution: Let x^3=a
So, x^6+63x^3-64
=(x^3)^2+63x^3-64,using A^MN=(A^M)^N
=a^2+63a-64,by substitution
=a^2+64a-a-64
=a(a+64)-1(a+64)
=(a+64)(a-1),taking (a+64) as common
=(x^3+64)(x^3-1),substituting back
=(x^3+4^3)(x^3-1^3)
=(x+4)(x^2-4x+4^2)(x-1)(x^2+1x+1^2),using A^3+B^3=(A+B)(A^2-AB+B^2),etc
=(x+4)(x^2-4x+16)(x-1)(x^2+x+1) Ans.