10th term of (X-2Y)^20?

Question

What is the 10th term of 10th term of (X-2Y)^20

Answer 1

the (k) th term of (x+y)^n
is
x^(n-k+1)y(k-1)(NCk-1)

using this we get

x^(20-10+1)(-2y)^9(20C9)

= - 2^9(20C9) x^11y^9

20C9 = 20!/(11!9!)

Answer 2

In general, the k(th) term of (A - B)^n is :

(-1)^(k-1) * A^(n-k+1) * B^(k-1) * n! / [ (k-1)! * (n-k+1)! ]

Letting k = 10, n = 20, A = X and B = 2Y gives the 10th term as :

(-1)^9 * X^(11) * (2Y)^9 * 20! / [ 9! * 11! ]

= -1 * X^11 * Y^9 * 2^9 * 167960

= - 85995520 * X^11 * Y^9

Answer 3

The 10th term is:

[20C(10-1)][x^(20-10+1)](-2y)^(10-1)
=(20C9)(x^11)(-2y)^9
=-512[20!/(9!*11!)](x^11)(y^9)

Answer 4

by binomial thearem we can find it.

t10=t9+1=20C9 . X^(20-9) .(2y)^9

=1007760.X^11.512Y^9

=515973120.X^11.y^9

Answer 5

Interesting question. You may want to read up on the Binomial Theorem. A general formula is:
(x+y)^n= sum (from k=0 to n) of (Binomial(n,k) * x^k * y^(n-k))
where Binomial(n,k) = n! / (k!(n-k)!)
n=20 and k=10 in your case.