Question

How do I use Pascal's triangle to expand the binomial `(d-3)^6`?

Answer 1

Pascal's Triangle looks like this:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1

Using the above numbers as coefficients,

`(d-3)^6`

`=1d^6 (-3)^0+6d^5(-3)^1+15 d^4(-3)^2+20 d^3(-3)^3+15 d^2(-3)^4+6 d^1 (-3)^5+1 d^0(-3)^6`

`=x^6-18x^5+135x^4-540x^3+1215x^2-1458x+729`