Multiplying Polynomials
[Show All Solutions]
Multiply each of the following.

1. ** **

Show Solution
Most people remember learning the
FOIL method of multiplying polynomials from an Algebra class. I’m not very fond of the FOIL method for the
simple reason that it only works when you are multiplying two polynomials each
of which has exactly two terms (*i.e.*
you’re multiplying two binomials). If
you have more than two polynomials or either of them has more or less that two
terms in it the FOIL method fails.

The FOIL method has its purpose,
but you’ve got to remember that it doesn’t always work. The correct way to think about multiplying
polynomials is to remember the rule that every term in the second polynomial
gets multiplied by every term in the first polynomial.

So, in this case we’ve got.

Always remember to simplify the
results if possible and combine like terms.

This problem was to remind you of
the formula

2. ** **

Show Solution
Remember that and so

This problem is to remind you that

so do not make that mistake!

There are actually a couple of
formulas here.

You can memorize these if you’d
like, but if you don’t remember them you can always just FOIL out the two
polynomials and be done with it…

3. ** **

Show Solution
Be careful in dealing with the 2
out in front of everything. Remember
that order of operations tells us that we first need to square things out
before multiplying the 2 through.

Do, do not do the following

It is clear that if you multiply
the 2 through before squaring the term out you will get very different answers!

There is a simple rule to remember
here. You can only distribute a number
through a set of parenthesis if there isn’t any exponent on the term in the
parenthesis.

4. ** **

Show Solution
While the second term is not a
polynomial you do the multiplication in exactly same way. The only thing that you’ve got to do is first
convert everything to exponents then multiply.

5. ** **

Show Solution
Remember that the FOIL method will
not work on this problem. Just multiply
every term in the second polynomial by every term in the first polynomial and
you’ll be done.