Question

Expand `(a+2b)^3` using the binomial theorum with steps?

Answer 1

`a^3 + 6a^2b+12ab^2+8b^3`

Explanation:

From Pascal's triangle (or factorial notation), the coefficients are:

1, 3, 3, 1

i.e. 1 for `a^3`, 3 for `a^2` and so on.

You then multiply the first time by `(2b)^0`, second term by `(2b)^1`, third term by `(2b)^2` and the final term is `(2b)^3`. I like to think of it as a pattern for these simple ones. There are some complicated formulae you can apply to every single expansion if you wish to research this further.