**If you're going on to Calculus, you're going to need these!**

**
Here's the first one:**

**Here's an example so you can
believe it:**

**Find this sum:**

**Now, find these sums and add them:**

**Do you believe it? (You
should have gotten the same thing for both.)**

**This may not seem like a big deal,
but you'll need it to prove some important calculus stuff, so let's
get used to it.**

**Here's the proof:**

Just expand it out... |

**Now, use the commutative and
associative properties... Gather up the
a's... Gather up
the b's...**

**Here are the other two properties
-- I'll let you do the proofs:**