Objectives: Review multiplying with exponents , the
distributive property , and multiplying polynomials.
Mini-Test 3 pushed back one week to Friday, March 2nd.
Multiplying Terms
Recall that in multiplying something like 2x^2 · 3x^4, we
can rearrange the order of the factors , multiply the
coefficients , and multiply the factors of x .
We generally just jump from the first step to the last .
Here are a few more examples.
For a product like 2x^2(x^3 + 3x), we can use the
distributive property.
We’ve done stuff like this before , but here are a few more
examples anyway.
Quiz 10, Part I
Multiply these out.
Multiplying polynomials in generarl
So far, we’ve used the distributive property, when one of
the polynomials has multiple terms. If polynomials
have multiple terms, we just use the distributive property as many times as we
need it. The simplest case
looks like
(9) (x + 2)(x+ 3) = x(x + 3) + 2(x + 3) = x · x + x · 3 +
2 · x+ 2·3 = x^2 + 3x + 2x + 6.
We can simplify further to x^2 + 5x + 6. You may have
heard the term “FOIL” used as a way to remember
this. F stands for firsts (x · x), O stands for outsides (x · 3), I stands for
insides (2 · x), and L stands for
lasts (2 · 3). I don’t really like the term FOIL very much, however. I don’t
like artificial ways of remembering
things, and I also don’t like that it only applies to a special case.
I think a better thing to remember is
Multiply every term in the first polynomial times every
term in the second.
This is true for any product of polynomials, no matter how
many terms there are. For example, consider the
following, where we take the first term times everything, the second term times
everything, and the third
term times everything.
We finish this off by combining like terms .
Here are two more examples .
Quiz 10, Part II
Multiply these out.
Homework 10
Multiply these out.
The fol lowing are worth three points each on the homework.
