Question

How many terms are there in the expansion of `(1+x)^8` ?

Answer 1

`9`

Explanation:

There are `9` terms in the standard form of the expansion of `(1+x)^8` - one for each power of `x` from `0` to `8` inclusive.

We can find the coefficients using the row of Pascal's triangle that starts `1, 8`

So:

`(1+x)^8=1+8x+28x^2+56x^3+70x^4+56x^5+28x^6+8x^7+x^8`

or in standard polynomial order:

`x^8+8x^7+28x^6+56x^5+70x^4+56x^3+28x^2+8x+1`