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Any mathematician to help me do this question.

Any mathematician to help me do this question.-example-1
User Rosenberg
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4 votes

9514 1404 393

Answer:

70

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).

_____

The value of nCk is n!/(k!(n-k)!). Then 8C4 is 8!/(4!)^2 = (8·7·6·5)/(4·3·2·1) = 70.

User Maneesh Srivastava
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