Question

How many distinct terms are there when
(1+x^7+x^13)^100 is multiplied out and simplified?

explain each step you did

Answer 1

(1+x^7+x^13)^100

= (x^13 + (1 + x^7) )^100

Answer 2

where did the 101 come from?

Answer 3

101+ 101!

Answer 4

again how do you even get 101 in the first place? please explain

Answer 5

if its to a power of 100 then there are 101 terms
1+x^7 would be to the power of 100, 99, 98, etc... meaning it would have 101! terms

Answer 6

are you sure? i find it hard to believe its 101! + 101 can you do a proof on that?

Answer 7

Hm I think its 101+ 100! now

Answer 8

lol i think i would want to see you do a proof on this if possible?

or if you can use combinatorics on this then please try it

Answer 9

Sorry I have no idea
I only just finished 12th grade maths

But like I said
(x^13 + (1 + x^7) )^100 has 101 terms
(1 + x^7) ^100 has (1 + x^7) to the power of 100, 99, 98, 97 etc,
But expanding (1 + x^7)^2 would give 3 terms --> We have already counted (1 + x^7) ^2 as one term, so essentially there are only 2 new terms --> therefore we minus 101

Making it essentially 101 + 100!

Answer 10

so you are saying there is 9.33x10^157 terms?

Answer 11

Yup..i think .@Skaematik is correct..)

Answer 12

The next step would be to find out any common factors of 13 and 7
But you can have some fun with that

Answer 13

sorry i find that answer hard to believe, its a huge number, i would say its has to be less than a million at most
im looking for a proof rather than just answering it that way

Answer 14

Try google, there is plenty of information on this