what is the term number

Question

Which term of the expansion of (x²+2)⁸ contains x¹⁰

term number is?

Answer 1

 

 

Answer 2

Which term of the expansion of (x^2+2)^8 contains x^10?

The Binomial Theorem says (x^2+2)^8 equals:

C(8,0) (x^2)^8 2^0 +
C(8,1) (x^2)^7 2^1 +
C(8,2) (x^2)^6 2^2 +

C(8,3) (x^2)^5 2^3 +
...
C(8,6) (x^2)^2 2^6
C(8,7) x^2 2^7
C(8,8) 2^8

So x^10 is in the 4th term if you count from 1, or the 3rd term if you count from 0.

 

The actual term is:

 

C(8,3) (x^2)^5 2^3

= (8!/(3!(8-3)!))(8x^10)

= (8*7*6*5!/(3*2(5)!))(8x^10)

= (8*7*6/(3*2))(8x^10)

= (8*7)(8x^10)

= 448 x^10