The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32 . What is the product of the two given numbers?

Expand and simplify the algebraic expression:

(x - 5)² + (x + 3)² + 4x

If $(x + {1\over x}) = \sqrt6 $, and x > 1, what is the value of $(x^8 - {1 \over x^8}) $?

If b = 5, determine the value of an expression $({5 \over b} + 5b)$ $({25 \over b^2} - 25 + 25b^2)$ using an identity.