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Find the coeffiecient of X3 in the expansion of (1+X)3(2+x2)10

a)2^10   b)2^12    c)2^14    d)2^16

asked in Mathematical Logic by Veteran (18.1k points)   | 59 views

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Just two cases Possible here :

1) Extract x from (1+X)3 and x2 from (2+x2)10 to finally get x3.  --> 3C10C* 29

2) Extract x3 from (1+X)3 and x0 from (2+x2)10 to finally get x3.  --> 3C10C* 210

So coefficient of x3 is --> case 1 + case 2 --> 30*29 + 210 --> 32 * 2--> 214.

answered by Loyal (3.5k points)  
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