4.10+Binomial+Theorem+(1-5)

We started out today with a discussion of why the parentheses were necessary in media type="custom" key="12019371"4.10 CYU #1b; however, I put that discussion in yesterday's wikipage, so you should go look there for the discussion.

Then we did several **more examples of expanding binomials.**


 * FIRST** we did an example that involved writing subtraction as adding a negative.

media type="custom" key="12019869"


 * SECOND** we did an example with a coefficient on both of the terms.

media type="custom" key="12019879"


 * THIRD** we looked at the coefficient of media type="custom" key="12019655" in the expansion of media type="custom" key="12019657" which is media type="custom" key="12019607" which is now in a form that can be evaluated on a calculator.

We also thought some more about how to factor expressions using a the binomial theorem:
Some expressions are relatively easy to factor because the binomial theorem/Pascal's triangle are still very visible:

media type="custom" key="12019685"

However, some expressions have Pascal's triangle more obscured. media type="custom" key="12019725"

In the expression above I cannot necessarily see the binomial theorem at first glance, but if I know that I need to factor this, then I might notice that the last term can also be viewed as media type="custom" key="12019721" and then I might choose to rewrite the expression like this:

media type="custom" key="12019737" which once again makes Pascal's triangle clear and now I can see that what I need to do is recognize that the expression above is the same as media type="custom" key="12019751".