Omit: Multiplying vertically and Examples 9 & 10
Note, we do not need to have like terms to multiply, just to add/subtract.
Objective 2: Multiply two binomials
To multiply two polynomials we need to multiply each term of the first polynomial by
each term of the second polynomial.
When multiplying a binomial by a binomial (something we will do a lot) a handy
process to use is the FOIL method .
First, Outside, Inside, Last.
We will need to combine like terms for our final answer.
Objective 3: Squaring Binomials
There are two ways to square (multiply by itself) a binomial: (a + b)2.
Or we can memorize this formula and use it in place of FOIL when you need to
If you have difficulty remembering the formulas, you can always use FOIL to
Warning! A very common error is
Objective 4: Multiplying the sum and difference of two terms
Here is another pattern that will come up often. Again you can either memorize the
formula or use the FOIL method.
FOIL: First, Outside, Inside, Last
Our goal is to rewrite polynomial expressions as being products of factors
than sums of terms.
Review: The difference between factors and terms
Objectives 1& 2: Identify and factor out the Greatest Common Factor (GCF)
Factoring is “un‐multiplying” 6 = 2 * 3
so 2 and 3 are factors of 6, and 2*3 is the factored form of 6.
The factored form of
the factored form of
The factors common to both monomials are so the GCF is
To factor out a GCF from a polynomial, we determine the GCF of the
terms and “un‐distribute” the GCF.
Our goal is the have an expression equivalent to the original polynomial, but
expression that is a product of a monomial (the GCF) and a simpler polynomial.
Note that if we were to multiply our result, we would have exactly what we
with so this is an equivalent expression but written in a different format .
Note also that 2 + 3y2 have no common factors.
Note: for the first example, the 1 is not optional!
Without having the 1 as a
placeholder, we would not have an equivalent expression…the second term of the
polynomial would be lost.
Can there be more than one correct factorization of a
There can be depending on the sign :