Multinomial Expansion

Can any one explain me how to find the coeff. of x5 in the expression
(1+x)(1+x+x2)(1+x+x2+x3+x4)2

I did not start Binomial Expansions yet.
So please explain in easy language.

10 Answers

11
Khyati ·

Binomial expansion se easy padega so learn that. If then too you aer unable to get then ask.

49
Subhomoy Bakshi ·

(1+x)(1+x+x2)(1+x+x2+x3+x4)(1+x+x2+x3+x4)

we have to find coeff of x5

so....we have to find all possible cases in which we have the result x5!!!
and the total number of cases would have given the coefficient since each trm has a coeff 1!!

4+5+4+5+4+3=15

tht is the answer i get!!

please verify!

1
swordfish ·

@Khyati - yes you are right, I will study BE next :)
@Subhomoy - answer is 25

1
nihal raj ·

ur concept correct ; just give time for highly basic things like addition!................................. :) just kidding

1
swordfish ·

lol @Nihal

1
swordfish ·

Can you explain me how you got that Subho?

49
Subhomoy Bakshi ·

hehe .. LOL!! yes i got the answer as 25 only...damn yaar!! :(

thats would be the reason if i do not get into KVPY this time! shit man! huh!

49
Subhomoy Bakshi ·

um...

look i just took the 1 in the first bracket....

and 1 from second bracket...found out possible cases in which we can get x5 from the rest of the 2 braces..

now took x from the 2 nd brac n found out ways of getting x4 from the rest braces

then took x2 from the 3nd bracket n found out ways of getting x3 from the braces...

next took x from the frst bracket and repeated...

this took about 2 mins time...but i think u can give that much time in an competitive exam behind certain +3 marks provided u can ensure unlike me that u won't do any ADDITION MISTAKE! :'(

1
swordfish ·

Thanks!

49
Subhomoy Bakshi ·

welcome![1]

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