If (a + b + c) ≠ 0, then (a + b + c) (a2 + b2 + c2 - ab - bc - ca) is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. a3 + b3 + c3 - 3abc.
(a + b + c) ≠ 0,
(a + b + c) (a2 + b2 + c2 - ab - bc - ca).................1
Let's assume a = b = c = 1
Put the value of a, b, and c in Equation 1
⇒ (1 + 1 + 1) (12 + 12 + 12 - 1 × 1- 1 × 1- 1 × 1)
⇒ (3)(3 - 3)
⇒ (3)(0)
= 0
Now option 3
a3 + b3 + c3 - 3abc
= 13 + 13 + 13 - 3 (1 × 1 × 1)
= 3 - 3 = 0
Only option 3 satisfies