Question

How do you use pascals triangle to expand `(x-3)^5`?

Answer 1

`x^5 - 15 x^4 + 90 x^3 - 270x^2 +405 x - 243`

Explanation:

We need the row that starts with `1\ 5`.

       1
    1 2 1
 1  3  3  1
1  4  6   4  1

1 5 10 10 5 1

`(x-3)^5`

`= x^5 + 5 x^4 (-3)^1 + 10 x^3 (-3)^2 + 10 x^2 (-3)^3 + 5 x (-3^4 )+ 3^5`

`= x^5 - 15 x^4 + 90 x^3 - 270x^2 +405 x - 243`