What is the first term in this expansion? a 2x15 b 215x15 c 10y15 d 1015y15
2 answers:
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Answer:
The correct option is;
False
Step-by-step explanation:
The coefficient of x^k·y^(n-k) is nk, False
The kth coefficient of the binomial expansion, (x + y)ⁿ is
Where;
k = r - 1
r = The term in the series
For an example the expansion of (x + y)⁵, we have;
(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵
The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15
Therefore, the coefficient of x^k·y^(n-k) for the expansion (x + y)ⁿ = not nk