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

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,

${\left(d - 3\right)}^{6}$

$= 1 {d}^{6} {\left(- 3\right)}^{0} + 6 {d}^{5} {\left(- 3\right)}^{1} + 15 {d}^{4} {\left(- 3\right)}^{2} + 20 {d}^{3} {\left(- 3\right)}^{3} + 15 {d}^{2} {\left(- 3\right)}^{4} + 6 {d}^{1} {\left(- 3\right)}^{5} + 1 {d}^{0} {\left(- 3\right)}^{6}$

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