TS EAMCET · Maths · Binomial Theorem
The coefficient of \(x^{12}\) in the expansion of \(\left(x^2+2 x+2\right)^8\) is
- A 1120
- B 2240
- C 2576
- D 4152
Answer & Solution
Correct Answer
(C) 2576
Step-by-step Solution
Detailed explanation
\(2n_1+n_2 = 12\), \(n_1+n_2+n_3 = 8\) For \((n_1, n_2, n_3) = (4, 4, 0)\): \(C_1 = \frac{8!}{4!4!0!} (2)^{4+0} = 70 \cdot 16 = 1120\) For \((n_1, n_2, n_3) = (5, 2, 1)\): \(C_2 = \frac{8!}{5!2!1!} (2)^{2+1} = 168 \cdot 8 = 1344\) For \((n_1, n_2, n_3) = (6, 0, 2)\):…
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