B.P.S.C. TRE-3 July, 2024
The quotient obtained when $a^3 + b^3 + c^3 - 3abc$ is divided by $a + b + c$ is -
a$a^2 + b^2 + c^2 - bc - ca + ab$
b$a^2 + b^2 + c^2 + bc + ca + ab$
c$a^2 + b^2 + c^2 - bc - ca - ab$✓ Correct
dMore than one of the above
eNone of the above
Explanation
$\because a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$ $\therefore \frac{a^3 + b^3 + c^3 - 3abc}{(a + b + c)} = \frac{(a^2 + b^2 + c^2 - ab - bc - ca)}{(a + b + c)}$ $= a^2 + b^2 + c^2 - ab - bc - ca$ Therefore, option (c) is the correct answer.
general-mental-ability