Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewMultiplying PolynomialsMultiply each of the following.1. ( 7x− 4)( 7x+4)SolutionMost people remember learning the FOIL method of multiplying polynomials froman Algebra class. I’m not very fond of the FOIL method for the simple reason that itonly works when you are multiplying two polynomials each of which has exactly twoterms (i.e. you’re multiplying two binomials). If you have more than twopolynomials or either of them has more or less that two terms in it the FOIL methodfails.The FOIL method has its purpose, but you’ve got to remember that it doesn’t alwayswork. The correct way to think about multiplying polynomials is to remember therule that every term in the second polynomial gets multiplied by every term in thefirst polynomial.So, in this case we’ve got.2 2( 7x− 4)( 7x+ 4) = 49x + 28x−28x− 16 = 49x− 16Always remember to simplify the results if possible and combine like terms.This problem was to remind you of the formulaa+ b a− b = a − b2. ( 2x − 5) 2Solution( )( )2 22Remember that 3 = ( 3)( 3)and so( ) ( )( )2 22x− 5 = 2x−5 2x− 5 = 4x − 20x+25This problem is to remind you thatnn( a−b) ≠a − b and ( a+ b)≠ a + bso do not make that mistake!( ) 2 22x−5 ≠4x− 25There are actually a couple of formulas here.2 2 2a + b = a + 2ab + bn n n n( )( )2 2 2a− b = a − 2ab+b© 2006 Paul Dawkins 16http://tutorial.math.lamar.edu/terms.aspx