Question

Without finding cubes, Factorise:(x-2y)cube+ (2y-3z)cube+ (3z-x)cube

Answer 1

There is an identity, if a+b+c=0, then a^3+b^3+c^3=3abc. In this case, if you add up the three terms inside the brackets, you'd get zero. So, the answer is equal to 3(x-2y)(2y-3z)(3z-x).