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

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Answer 1 · 2014-09-28T12:16:09

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,

$(d-3)^6$

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

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

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