Mathematics

Problem

Understanding the structure of cube identities. a. (i) Write the expansion of

(a + b)^3

. b. (ii) Rearrange the expansion obtained in part (i) to express

a^3 + b^3

in terms of

(a + b)

and

ab

. c. (iii) Explain why

a^3 + b^3

is always divisible by

(a + b)

for all real numbers

a

and

b