Question

Find the coefficient of the indicated term in each expansion. (2x – y)4, x2y2 term

Answer 1

Answer:

  24x²y²

Step-by-step explanation:

For k=0 to n, the k-th term of (a+b)^n is ...

  (nCk)·a^(n-k)·b^k

You want the k=2 term for the n=4 expansion with a=2x and b=-y.

Then the third term of the expansion is ...

  (4C2)·(2x)^2·(-y)^2 = 6·4x^2·y^2 = 24x^2y^2

_____

nCk = n!/(k!(n-k)!)

4C2 = 4!/(2!·2!) = (4·3)/(2·1) = 6