## Troubles with Tri…angles

You have been warned – any damage to your social status is your past this point is your own responsibility.

You have been warned!

In an original series episode of Star Trek, the crew of the Enterprise encountered cute little balls of fluff – called Tribbles. Listen to them:

These “Tribbles” had one downside – they were T.R.O.U.B.L.E – the episode was called “The Trouble with Tribbles” and that trouble was that they never stopped breeding – until all the available space was occupied by tribbles.

This is similar to Pascal’s Triangle – it goes on forever and takes up every last little bit of space. Each line is longer than the last and ocntains bigger numbers:

Each element is created by the pair of elements above it, like this:

But what good is it? Well it has alot of number patterns (also here) in it, but the one we are interested in is how to use it to expand binomial expressions. Binomial expressions are expression of the form (a + b)^n, such as (x + 1)^2. These are easy to expand – but you have to do it the right way. i.e. not like this:

This is a much better way to do it:

Finally, here are some notes that you can use to supplement your notes and understanding of chapter 4 (1, 2)

Good luck & see you in class!

ps. Pascal didn’t invent the Triangle named after him – he just expanded on it’s uses.