Apalimage of a natural number is the number which has the same digits but in reverse order. for example, 659 and 956 are palimages; so are 1327 and 7231. now add 354 and its palimage. call this sum x. add x and its palimage. call this sum y. add y and its palimage. call this sum z. what is the value of z?

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb