Question

What is the 6th term in the expansion of `(3a^2 - 2b)^10`?

Answer 1

`t_6 = -1,959,552a^10b^5`

Explanation:

When finding specific terms in a binomial expansion, we need to use the formula `T_(r + 1) = color(white)(two)_nC_r xx a^(n - r) xx b^r`, where `t` is the term in the expansion of `(a + b)^n`.

Let's start by solving for `r`.

`r + 1 = 6 -> r = 5`

`t_6 = color(white)(two)_10C_5 xx (3a^2)^5 xx (-2b)^5`

`t_6 = -1,959,552a^10b^5`

Footnote:

The formula `color(white)(two)_nC_r` represents `(n!)/((n - r)!r!)`, where `!` is factorial. By definition, `(n!)= n(n - 1)(n - 2)...(1)`.

Hopefully this helps!