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The coefficient of t^32 in the expansion of (1+t^2)^12(1+t^12)(1+t^24)

The coefficient of t^32 in the expansion of (1+t^2)^12(1+t^12)(1+t^24)

Grade:11

1 Answers

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137 Points
6 years ago
We can write it as (1+t^2)^12(1+t^12+t^24+t^36) , the general term of this is 12Cr.t^2r(.....) Now after that compare the power of t as 0+2r=32, 12+2r=32, 24+2r=32 and by this we get value as r=16, r=10, r=4 . r=16 is not possible because the coefficient is 12Cr therefore possible value of r are as 10,4 . Therefore the coefficient is 12C10+ 12C4 = 561

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