Question

What is the fourth term in the expansion of `(2x-y)^5`?

Answer 1

You can find this by using the formula `t_(r + 1) =_nC_r xx a^(n - r) xx b^r`

Explanation:

r can be found by solving the simple equation `t_(r + 1) = 4` We can immediately eliminate the t, and we find that r is 3. n is the exponent, which is 5 in this case. Note the n and the r are in base at the C.

`t_4 =_5C_3 xx 2x^(5 - 3) xx -y^3`

`t_4 = 10 xx 4x^2(-y^3)`

`t_4 = -40x^2y^3`

Your fourth term is `-40x^2y^3`.

Practice exercises:

1. Find the 7th term in `(-2x + 3y)^12`

2. Find the middle term of `(3x - y^3)^8`

Good luck!