What is the coefficient of \(a^2b^2\)in \((a+b)^4\left(c+\dfrac{1}{c}\right)^6\)?

Jz1234
Aug 26, 2017

#1**+2 **

Let's look at the expansion of the second term, first

Note that, by the binomial expansion, the fourth term of this expansion will be :

20 c^3 (1/c)^3 = 20

And note that every other term in this expansion either contains "c" or "1/c" - or both - to some power(s)

And in the expansion of (a + b)^4 , the a^2b^2 term will be the third term....and its coefficient will be 6

So.....the a^2b^2 term in the product of both expansions will be 20 * 6 = 120

CPhill
Aug 26, 2017