9514 1404 393
Answer:
240
Explanation:
The generic k-th term of the expansion of the binomial ...
(a +b)^n
is given by ...
(nCk)a^(n-k)b^k . . . . . where nCk = n!/(k!(n-k)!) and 0 ≤ k ≤ n
For this problem, we have ...
a=2x, b=y, n=6, k=2
Then the 2nd term (counting from 0) is ...
6C2×(2x)^4×y^2 = (6·5)/(2·1)·16x^4·y^2
= 240x^4y^2
The desired coefficient is 240.
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Additional comment
The coefficients for the expansion match the numbers in a row of Pascal's triangle. The row beginning with 1, n will have the coefficients for the expansion to the n-th power.