Question

Which statement about the binomial expansion of (x2 – x)9 is true?

The first term is –x18.

The second term is 9x17.

The third term is 36x14.

The last term is –x9.

Answer 1

D

Explanation:

just took it

Answer 2

Option D.

Explanation:

The given expression is

`(x^2-x)^9`

Here, n=9, p=x^2 adn q=-x.

kth term in the binomial expansion of
`(p+q)^n` is

`T_(r)=^nC_(r-1)p^(n-r+1)q^(r-1)`

First term of the binomial expansion of
`(x^2-x)^9` is

`T_(1)=^9C_(1-1)(x^2)^(9-1+1)(-x)^(1-1)=x^(18)`

Second term of the binomial expansion of
`(x^2-x)^9` is

`T_(2)=^9C_(2-1)(x^2)^(9-2+1)(-x)^(2-1)=9(x^16)(-x)=-9x^(17)`

Third term of the binomial expansion of
`(x^2-x)^9` is

`T_(3)=^9C_(3-1)(x^2)^(9-3+1)(-x)^(3-1)=9(x^14)(x^2)=36x^(16)`

Last or 10th term of the binomial expansion of
`(x^2-x)^9` is

`T_(10)=^9C_(10-1)(x^2)^(9-10+1)(-x)^(10-1)=1(x^0)(-x^9)=-x^(9)`

Therefore, the correct option is D.