+50 What is the coefficient of \(a^2b^2\)in \((a+b)^4\left(c+\dfrac{1}{c}\right)^6\)?
+129850
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
