Question

Binomial Expansion.
Find the term independent of x in the expansion of
[(x^2) + (2/x)]^6

Answer 1

What do we define as independent of x?

Answer 2

the term would not contain x

Answer 3

Okay, or answer for him @cwrw238 :P

Answer 4

(r + 1)th term of ( a + b)^n = nCr a^(n-r) b^r

Answer 5

looks like the 5th term

(4 + 1)th term = 6C4 (x^2)^6-4 (2/x)^4
= 15 x^4 * 16 / x^4
= 240

Answer 6

how do you know it is the 5th term ?

Answer 7

good question - the power of x in x^2 and x in 2/x had to be the same . To be honest it was an inspired guess.

Answer 8

i need a real way to solve this =.= thanks for the help though!

Answer 9

i'll give it some more thought .. the answer is correct though.

Answer 10

yes the answer is 240!, thanks much! :)

Answer 11

OK

go back to the fornula

(r + 1)th term = nCr a^(n-r) b(^r for the binomial expansion of (a + b)^2

here we have x^2(n-r) and 2^2 / x^r

and n = 6

so for x to be eliminated we need 2(6 - r) = r

solve for r: 12 - 2r = r

12 = 3r
so r = 4

therefore we need the (4 + 1)th term
ie the 5th term


the other way to do this would be to expand the whole expression until you reach the term where x is eliminated

Answer 12

* 4th line - it should read 2^r / x^r

Answer 13

- not that this makes any difference to the process

Answer 14

hope this is clear to you

Answer 15

ok got it, thanks a bunch !

Answer 16

yw - that ones a bit tricky