AoPS

MATHEMATICS · Multi-part · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Let

A=(x+2y)^3+(x-2y)^3-2x^3

. (i) Expand

A

completely and simplify the result. (ii) Factorise the simplified expression obtained in part (i). (iii) Hence show that

A

is divisible by

12xy^2

for all real values of

x

and

y

. State clearly the factor(s) that establish this divisibility.