THIS USER ASKED 👇

Which statement about the binomial expansion of (x2 – x)9 is true? the first term is –x18. the second term is 9×17. the third term is 36×14. the last term is –x9.

THIS IS THE BEST ANSWER 👇

Option D.

Step by step explanation:

The sentence is given

(x ^ 2-x) ^ 9

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

kth term in binomial extension on (p + q) ^ n is

T_ {r} = ^ nC_ {r-1} p ^ {nr + 1} q ^ {r-1}

The first term of binomial expansion on (x ^ 2-x) ^ 9 is

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

The second term of the binomial expansion on (x ^ 2-x) ^ 9 is

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

The third term of binomial expansion on (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}

The 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, D. is the right choice