Let us distribute evenly over the land of polynomials

Let us distribute the multiplicative bliss evenly over the land of polynomials, thus sayeth the algebra queen of the realm.

Today's lesson involves multiplying polynomials times polynomials. Here once again we need to stress the need to multiply EVERY term in the first polynomial quantity times EVERY term in the second polynomial quantity.

Parentheses will be seen in these problems wrapped around the polynomials.

To simplify this product, we must multiply the x in the first quantity times BOTH the x and the 5 in the second quantity.

Then we must use the 3 and multiply it times BOTH the x and the 5. It will look like this.

This same approach is used even if the polynomials involved are longer. Just remember to watch your signs carefully and add all like terms after multiplying.

Take a look at this example:
Step2 is usually optional.

Now back in ancient mathematical history, like the 1960's and 70's, people used to use a little acronym to help them multiply two binomials together mentally.

It was called the FOIL method. The letters reminded you what order to multiply the terms so that you did not leave anything out.

Let's consider the above example again.
F reminds you to multiply the first terms in each binomial (the two x's in our example).
O tells you to multiply the outside terms in each binomial (the first x and the 5).
I reminds us to multiply the inside terms (the 3 and the second x).
L tells us to multiply the last terms (the 3 and the 5).

Often the O and the I will be like terms and you can add them together.
So the mental trick is:

Write down the first product
Get the outside product and indside products, and add them together if possible. Then write the result beside the first product.
Finally write down the last product.

Let's try a few. Click the answer link to see if you are correct.

Click HERE for the answers.

We hope these are what you got!

BACK