Question

Expand (n-4)^6

Answer 1

can you expand (n-4)^2, then you have 3 of those left

(n-4)^6 = ((n-4)^2 )^3

Answer 2

lots of keeping track of powers of n

Answer 3

you should get to these as the coefficients for x^6 town to x^0

1 -24 240 -1280 3840 -6144 4096

Answer 4

Available Answers:

A: \[n^6-24n^5+240n^4-1280n^3+3480n^2-6144n+4096\]

B: \[n^6+24n^5+240n^4-1280n^3+3480n^2-6144n+4096\]

C: \[n^6-24n^5+240n^4-1290n^3+3840n^2-6144n+4096\]

D: \[n^6-24n^5+240n^4-1280^3+3480n^2-6144n+5000\]

Answer 5

Apologies for taking so long, it's a lot of numbers to type out.

Answer 6

oh.. ha you didnt have to, or take a screen shot instead maybe

Answer 7

if you can expand things without problem i would just use a algebra system to do it for you

Answer 8

Expanding things is a bit of a problem for me.

Answer 9

it is everything from one quantity multiplied to everything from the other quantity like for this with only 2 terms in each, take 2 of the 6

(n - 4)^2 = (n-4)*(n-4) = n^2 - 4n - 4n + 16

(n-4)^2 = n^2 - 8n + 16

Answer 10

gets to be not fun

Answer 11

I see.

Answer 12

u can also use the binomial expansion :)

Answer 13

What is the binomial expansion?

Answer 14

Also I think the answer is A.

Answer 15

Okay.

Answer 16

what was the pascal triangle for again, i was thinking about that on this one

Answer 17

although for sure not applied

Answer 18

I think it's for finding answers to problems like this one.

Answer 19

i thought they were symmetrical for the numbers

Answer 20

okay
so binomial expansion is like a general formula to expand \((a+b)^n\)
it says that-
\((a+b) ^n=~^nC_0(a)^{n-0}(b)^0+~^nC_1(a)^{n-1}(b)^1+~^nC_2(a)^{n-2}(b)^2+........+~^nC_n(a)^{n-n}(b)^n\)

Answer 21

Sounds good.

Answer 22

okay and we just gotta figure out what is our \(a\),\(b\) and \(n\) from \((n-4)^6\) and just substitute it in the equation :)

Answer 23

I think that A would be N, B would be -4 and N would be exponent six?

Answer 24

yes n will be 6
now just put those values in the equation and try to simplify it

Answer 25

That was long. I ended up with the string of numbers associated with the first answer.

Answer 26

how can you know if you can take some ugly thing and go back the other way to a simple higher power single binomial?

Answer 27

If you can get there in the first place?

Answer 28

you can take binomial expansion method when you already don't know the expansion formula :)
like here i didn't knew what is the formula to (a+b)6 so i used binomial expansion

Answer 29

Okay. I'll use that.

Answer 30

Thanks for the help, by the way.

Answer 31

np :)

Answer 32

Well, after I wrote it down, and tried it out again, I ended up with \[n^6-24n^5+240n^4-1280^3+3840n^2-6144n+4096\]

Answer 33

if they gave you a string of powers like that, maybe any number of em, is it possible to prove you can put that into some simpler polynomial thing

Answer 34

or prove you cant, either case

Answer 35

Let me see.

Answer 36

like a 10^(42) term polynomial, can that be factored into some simpler form

Answer 37

I don't think so.

Answer 38

well if it follows this binomial coefficients , it can but, ah nvm, just thinking

Answer 39

I'll definitely need to work on this subject.

Answer 40

I'll just close the problem, if it's alright with you. Thank you for all your help! :)