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

A. 1
B. 40
C. 70
D. It does not exist

User Galmok
by
4.8k points

1 Answer

3 votes

Answer:

C. 70

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.

User Biegleux
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5.1k points