This question was previously asked in

SSC CGL Previous Paper 66 (Held On: 3 March 2020 Shift 2)

Option 3 : 6a(a – b + c) (c – a – b)

Cell

345924

10 Questions
10 Marks
7 Mins

**GIven:**

(a + b – c)^{3} + (a – b + c)^{3} – 8a^{3}

**Concept used:**

Trial and error

**Calculation:**

Let us use the trial and error method to obtain the solution.

Let a = b = c = 1

Then,

(a + b – c)3 + (a – b + c)3 – 8a3 = 1 + 1 – 8 = (-6)

Now, lets check option (1):

3a(a + b – c)(a – b + c) = 3 × (1) × (1) ≠ (-6)

Now, lets check option (2):

6a(a + b – c) (a – b + c) = 6 × (1) × (1) ≠ (-6)

Checking option 3^{rd}.

6a(a – b + c) (c – a – b) = 6 × 1 × (-1) = (-6)

Hence, option 3 is right.

**∴ The solution of the question is 6a(a – b + c) (c – a – b). **