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

1 Answer
Wataru
Sep 28, 2014

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(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=1d6(−3)0+6d5(−3)1+15d4(−3)2+20d3(−3)3+15d2(−3)4+6d1(−3)5+1d0(−3)6

=x^6-18x^5+135x^4-540x^3+1215x^2-1458x+729=x6−18x5+135x4−540x3+1215x2−1458x+729

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