Question

What is the coefficient of x^4y^4 in the expansion (x+y)^8?

Answer 1

Answer:

  C.  70

Step-by-step explanation:

In the expansion of (a + b)^n, the k-th term is ...

  nCk·a^(n-k)b^k . . . . . k = 0 to n; nCk = n!/(k!(n-k)!)

Here, we have n=8, k=4, so the term of interest is ...

  8C4·x^4y^4 = (8·7·6·5)/(4·3·2·1)x^4y^4 = 70x^4y^4

The coefficient of the term is 70.