Post on 28-Dec-2015
MTH 065Elementary Algebra II
Chapter 5 – Polynomials
Section 5.6 – Special Products
Copyright © 2008 by Ron Wallace, all rights reserved.
NOTE!NOTE!
Important skills in mathematics … Categorizing types of problems. Recognizing patterns. Special cases of more general problems.
This section … 5 special products Two binomials Two “similar” binomials A sum and difference of two terms Squaring a sum Squaring a difference
The “FOIL” method! First Outside Inside Last
ac ad bc bd
Product of Two Binomials
( )( )a b c d F L
IO
The “FOIL” method! First Outside Inside Last
22 8 3 12x x x
Product of Two Similar Binomials
(2 3)( 4)x x F L
IO
22 5 12x x
LikeTerms
1st terms are like terms2nd terms are like terms
The “FOIL” method! First Outside Inside Last
2 2a ab ab b
Sum & Difference of Two Terms
( )( )a b a b F L
IO
2 2a b
Opposites
The “FOIL” method! First Outside Inside Last
2 2a ab ab b
Squaring a Sum
( )( )a b a b F L
IO
2 22a ab b
Same
2( )a b
The “FOIL” method! First Outside Inside Last
2 2a ab ab b
Squaring a Difference
( )( )a b a b F L
IO
2 22a ab b
Same
2( )a b
Summary …
( )( )a b c d ac ad bc bd
2( )( ) ( )rx s mx n rmx rn sm x sn
2 2( )( )a b a b a b
2 2 2( ) ( )( ) 2a b a b a b a ab b
2 2 2( ) ( )( ) 2a b a b a b a ab b
F O I L