Question

in the expansion of (x^2+3)^10 what is the coefficient of the term containing x^16. I did 10c4 * 3. But i am not getting the correct answer. can someone please show me how to do this. thanks for your time!

Answer 1

the general term is
GT(n+1) = C(10,n)(x^2)^n (3)^(10-n)

= C(10,n)(x)^2n (3)^(10-n)

so the x^16 has to come from the x^2n
and 2n = 16
n = 8

so it is term(9) and it is
C(10,9)(x^2)^8 (3)^(10-8)
= 10(x^16)(9)
= 90x^16

so the coefficient is 90

Answer 2

<<
so it is term(9) and it is
C(10,9)(x^2)^8 (3)^(10-8)
= 10(x^16)(9)
= 90x^16

so the coefficient is 90 >>

should have said:

so it is term(9) and it is
C(10,8)(x^2)^8 (3)^(10-8)
= 45(x^16)(9)
= 405x^16

so the coefficient is 405

Answer 3

thanks!