Question

What is the 6th term in the expression (2x-y)^10

Answer 1

Hello from MrBillDoesMath!

Answer:

- 8064 x^5 y^5

Discussion:

The binomial theorem gives us the expansion  of  (a + b) ^n  :

(a + b ) ^n

= a^n + na^(n-1)b +  (n(n-1)/ 2!) a^(n-2)b^2 +....

In our case, taking the 6th term above, setting a = 2x, b = -y, and n = 10 gives

( (10*9*8*7*6)/ (5 *4*3*2*1) )  * (2x)^5 (-y)^5r

=  - 8064 x^5 y^5

Thank you,

MrB