# Thread: binomial coefficients/Pascal triangle shortcut with a negative?

1. ## (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?

2. ## Re: binomial coefficients/Pascal triangle shortcut with a negative?

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.
$(x-2y)^5=x^5+5x^4(-2y)+10x^3(-2y)^2+10x^2(-2y)^3+5x(-2y)^4+(-2y)^5$.

3. ## Re: binomial coefficients/Pascal triangle shortcut with a negative?

Originally Posted by Plato
Here is an example.
$(x-2y)^5=x^5+5x^4(-2y)+10x^3(-2y)^4+10x^2(-2y)^3+5x(-2y)^4+(-2y)^5$.
Thanks, that makes sense!

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### pascal negative triangle

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