Question

Derivation of algebraic identity cube of a +cube of b+cube of c - 3 abc= (a+b+c)( square of a+square of b+ square of c-ab -bc-ca)

Answer 1

Step-by-step explanation:

The basic formula is

(a+b)3=a^3 +b^3+3^ab(a+b)

Rearranging the terms to obtain the desired result we get;

a^3+b^3=(a+b)3–3^ab(a+b)

Simplifying it further by taking (a+b) common we obtain,

a^3+b^3

=[a+b] [(a+b)2–3^ab(a+b)]

=[a+b] [a^2+b^2+2ab-3ab] (expanding (a+b)2)

=[a+b] [a^2-ab+b^2]

THIS IS THE BEST EXPRESSION FOR THIS QUESTION(THOUGH IT SEEMS LENGTHY)