Which term of the expansion of (x^4 + 4 )^{16} contains x^{28}? I had gotten 2998927360, but that seems to be wrong. Medal to the winner.

Question

anonymous · Answer

Same question, but (x+1)^9 containing x^6. I got 84 in my attempt.

anonymous · Answer

are you asking which term or what is the term's coefficient? the coefficeint for (x+1)^9 with x^6 is 84. ya.

anonymous · Answer

I am asking for it's coefficient.

campbell_st · Answer

oops should read 

$$^{28}C_{21}(x^4)^{28-21}4^{21}$$

the reason is 

using the power of a power you get 

$$(x^4)^7=x^{4 \times 7} = x^{28}$$

and then use the binomial expansion...

anonymous · Answer

I'm getting 92358976733184 x^28. I think I simplified wrong.

campbell_st · Answer

well it will be a huge number... just because of the silliness of the question. I haven't worried about calculating... 

other than 11 84040 x 4^21

anonymous · Answer

Sorry, is that 11(84040)(4^21) or 1184040x4^21?

campbell_st · Answer

oops wrong power 

so its

$$^{16}C_{9}(x^4)^{16-9}4^9$$

so its 

2998927360 x^28

campbell_st · Answer

I misread the power of the binomal, I read it as 28.. should be 16... which reduces the size of the coefficient...

anonymous · Answer

But that is the answer I had submitted before and it claimed it to be wrong.

anonymous · Answer

It's in my question. I submit my answers on this website, and I get 5 tries. It tells me when what I submitted was wrong.

campbell_st · Answer

ummm well its the right method..and I just used wolfram alpha to check and it came up with 

2998927360

campbell_st · Answer

so perhaps there is a typo in the question or the recorded answer.

anonymous · Answer

I'll snap-shot the question, perhaps I typed it out wrong. Mind if I tag you in it?

campbell_st · Answer

thats fine... just post it here and I'll wait

anonymous · Answer

Never mind, I'll just post it here. Silly me.

anonymous · Answer

attachment

campbell_st · Answer

well I wouldn't have found the coefficient 

my guesses are 

8th term 

or the binomial expansion 

$$^{16}C_{9}(x^4)^{16-9}(4)^9$$

anonymous · Answer

I tried "8" (they don't let me put "th"), so that one is out.

campbell_st · Answer

wow.... that was my strongest choice... 

sorry I can't help more... you certainly seem to have the understanding... its a shame the question isn't more descriptive about the method of answering...

anonymous · Answer

It's true. I do understand the method, that is why I was surprised when my answers were not accepted. I'll ask my teacher about it. Thanks. I'll leave this open if something pops into your head though.

campbell_st · Answer

good luck