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