9514 1404 393
Answer:
70
Step-by-step explanation:
If we consider the terms to have decreasing powers of x, then the middle term is the one with x^4y^4 as its variables. The full value of that term is ...
(8C4)(2x)^4(3y)^4 = 70(6xy)^4
Substituting for x and y, this is ...
70(6(1/3)(1/2))^4 = 70(1^4) = 70
The middle term is 70 when (x, y) = (1/3, 1/2).
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The value of nCk is n!/(k!(n-k)!). Then 8C4 is 8!/(4!)^2 = (8·7·6·5)/(4·3·2·1) = 70.
