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

 Aug 26, 2017
 #1
avatar+102408 
+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

 

 

cool cool cool

 Aug 26, 2017
edited by CPhill  Aug 26, 2017
edited by CPhill  Aug 27, 2017

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