MCQ
The expression (a - b)3 + (b - c)3 + (c - a)3 can be factorized as:
- A(a - b)(b - c)(c - a)
- B3(a - b)(b - c)(c - a)
- C-3(a - b)(b - c)(c - a)
- D(a + b + c)(a2 + b2 + c2 - ab - bc - ca)
✓
Answer
- 3(a - b)(b - c)(c - a)
Solution:
By we know that a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
If a + b + c = 0, then
a3 + b3 + c3 = 3abc
In given expression,
Let a - b = A, b - c = B, c - a = C
Now, a - b + b - c + c - a = 0
i.e. A + B + C = 0
⇒ A3 + B3 + C3 = 3ABC
⇒ (a - b)3 + (b - c)3 + (c - a)3 = 3(a - b)(b - c)(c - a)
Hence, correct option is (b).
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