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 what is the sum of the coefficents of the even degrees of the product of \((-\frac{3}{2}x^2+\frac{1}{2}x+4)^{16}\)

 Jul 4, 2020
 #1
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-1

(43046721 x^32)/65536 - (14348907 x^31)/4096 - (157837977 x^30)/8192 + (518154975 x^29)/4096 + (4068180855 x^28)/16384 - (8827766451 x^27)/4096 - (14523632991 x^26)/8192 + (94257891351 x^25)/4096 + (220712269635 x^24)/32768 - (706381131105 x^23)/4096 - (23495103567 x^22)/8192 + (3940745861637 x^21)/4096 - (1959573354921 x^20)/16384 - (16925275164105 x^19)/4096 + (6150417128055 x^18)/8192 + (57033142395909 x^17)/4096 - (166621058538623 x^16)/65536 - (19011047465303 x^15)/512 + (683379680895 x^14)/128 + (626862043115 x^13)/8 - (24192263641 x^12)/4 - 129736489272 x^11 - 1031335136 x^10 + 165371348480 x^9 + 17223697920 x^8 - 156919300096 x^7 - 32238338048 x^6 + 104507375616 x^5 + 32107397120 x^4 - 43620761600 x^3 - 17716740096 x^2 + 8589934592 x + 4294967296.

 

Well young person, here is something that will keep you busy for a while!! Just add up all the coefficients  of even terms and you got full marks, if you don't make a mistake! Good luck to you

 Jul 4, 2020
 #2
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+1

Um how is a person supposed to add all of that?

gwenspooner85  Jul 4, 2020
 #3
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if we plug in 1 into this we can find the sum of all the coefficents which is 3^16 and if we plug in -1 into the equation we have the same thing except that the odd terms are negitive becasue -1 to the power of any odd term would make it negitve and even makes it even, and plugging in -1 we get 2^16 now add these values together we get what we want multiplied by 2 so then we divide it all by to giving us the answer: (3^16+2^16)/2 you can do that complicated part on your own cheeky.

 Jul 5, 2020

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