Binomial expansion

Hello, and welcome to FMH! :)

What do you mean by the \(n=12\) term?
 
(a+b)6 = 1a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + 1b6

What is the expression for a and b in your problem. I will give an invaluable hint. What is in between ( and + is your a and what is in between the + and ) is your b.

Just plug that into the formula I wrote above for a and b. Please post back.
 
Thank you!

I'm not for sure so that's why I'm trying to find out. The problem says:
Find the n=12 term of the expansion of the binomial (3x+y)^6
 
Jammit55 said:
Thank you!

I'm not for sure so that's why I'm trying to find out. The problem says:
Find the n=12 term of the expansion of the binomial (3x+y)^6
Click to expand...
Please practice multiplying it out. Possible after doing that you might see the answer which includes knowing that there is no answer.

Are you sure the problem say n=12 term and not n=12th term?
 
Ok so I figured that my a=3 and b=1. I times it all out and got 4096. Does that sound reasonably right?
 
Jomo said:
Please practice multiplying it out. Possible after doing that you might see the answer which includes knowing that there is no answer.

Are you sure the problem say n=12 term and not n=12th term?
Click to expand...
Are you perchance saying that there might not be an answer? I expanded the binomial and the closest number I got to it was 18xy^5. But that's definitely not 18 so could it be possible that there isn't an answer?
 
Don't necessarily blame the answer for not existing. There isn't even a coefficient of 12. Sorry, you'll definitely need a better question.
 
Jammit55 said:
Ok so I figured that my a=3 and b=1. I times it all out and got 4096. Does that sound reasonably right?
Click to expand...
No! a is everything and i mean everything between the left parentheses and the plus sign. b is everything between the plus and the right parentheses.

4096 is an exact value! You do NOT know the value of 3x and y hence you do not know what 3x+y is yet you know the value of (3x+y)^6? Do you believe that? Do you think that I was just wasting my time writing out that long formula.

One last question? Is (2x+3)^2 simply (2+3)^2 = 5^2=25. So x can just be ignored? Hmm, I wonder why we are always solving for x. I am not saying this to be less than nice but rather to get you to think.

Now please multiply out (3x+y)^6.
 
Jammit55 said:
Are you perchance saying that there might not be an answer? I expanded the binomial and the closest number I got to it was 18xy^5. But that's definitely not 18 so could it be possible that there isn't an answer?
Click to expand...
Im confused now. If you know how to expand the binomial then how did you get 4096?

Please post what you got in your expansion, please.
 
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