Download Section 4.5 Multiplication of Polynomials

Multiplying Polynomials
Exponents
Remember if you are multiplying numbers
with the same base, then ADD the
exponents together.
Examples:
x x  x
2
3
5
y y  y
4
6
10
We will learn how to multiply the following:
-A monomial and a polynomial
-A binomial and a binomial
-A binomial and a trinomial
-A trinomial and a trinomial
*Always write your answers in
standard form!
Multiplying a Monomial by a Monomial
( 4a )(2a )  ( 4  2)(a  a )  8a
2
3
2
3
(3b )(5a )  (3  5)(b a ) 
5 2
2 5
15b a  15a b
5
2
5
2
5
Multiplying a Monomial and a Binomial
( 4)(2a  3)  8a  12
2
2
Note that a (monomial)(binomial) = binomial
(1)(2) = 2
Multiplying a Monomial and a Trinomial
( 2b )(b  3b  5)  2b  6b  10b
2
3
2
Note that a (monomial)(trinomial) = trinomial
(1)(3) = 3
Multiplying Two Binomials
( a  b)(c  d )  ac  ad  bc  bd
Note that a
(binomial)(binomial) = 4-nomial
(2)(2) = 4
Multiplying Two Binomials
Combine like terms
2
( x  4)( x  1)  x  x  4 x  4
 x  5x  4
2
FOIL Method
*works for a binomial times
binomial
First
Outer
Inner
Last