What is the coefficient of a^b^4 in the expansion of (a + b)^12?
Correct answer: B. 495
- A. 494
- B. 495
- C. 496
- D. 497
Explanation
The correct answer is b) 495.The general term of the binomial expansion of (a + x)^r is given as:Tr+1 = (r!(a)^(r-r)(x)^rThe given expression is: (a + b)^12.The general term for the binomial expansion of this expression would be:Tr+1 = (12!)(a)^(12-r)(b)^rAccording to this formula, r must be equal to 4 if we want to obtain the term with a^b^4.Using r = 4, we get:T4+1 = (12!)(a)^(12-4)(b)^4T4+1 = (12!)(a)^8(b)^4So, the coefficient of a^b^4 is (12!)/4! = 12C4 = 495.Therefore, the coefficient of a^b^4 in the expansion of (a + b)^12 is 495.
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