# binomial coefficients/Pascal triangle shortcut with a negative?

• Sep 30th 2011, 12:55 PM
delgeezee
(solved)binomial coefficients/Pascal triangle shortcut with a negative?
I am learning how to expand binomial coefficients using Pascal's Triangle.
All the examples I see are when 'a' and 'b' are positive. What is the trick in terms of signs when either 'a' or 'b' is negative?
• Sep 30th 2011, 01:24 PM
Plato
Re: binomial coefficients/Pascal triangle shortcut with a negative?
Quote:

Originally Posted by delgeezee
I am learning how to expand binomial coefficients using Pascal's Triangle.
All the examples I see are when 'a' and 'b' are positive. What is the trick in terms of signs when either 'a' or 'b' is negative?

Here is an example.
\$\displaystyle (x-2y)^5=x^5+5x^4(-2y)+10x^3(-2y)^2+10x^2(-2y)^3+5x(-2y)^4+(-2y)^5\$.
• Sep 30th 2011, 01:40 PM
delgeezee
Re: binomial coefficients/Pascal triangle shortcut with a negative?
Quote:

Originally Posted by Plato
Here is an example.
\$\displaystyle (x-2y)^5=x^5+5x^4(-2y)+10x^3(-2y)^4+10x^2(-2y)^3+5x(-2y)^4+(-2y)^5\$.

Thanks, that makes sense!