Question

Can you help me please ​

Answer 1

9514 1404 393

Answer:

  240

Step-by-step 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.