# Algebra-Trigonometry-CynthiaYoung-3ed7.pdf - 8/3/12 11:16...

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0.3Polynomials: Basic Operations31EXAMPLE 5Multiplying Two PolynomialsMultiply and simplify=2x2(x2-5x+7)-3x(x2-5x+7)+1(x2-5x+7)(x2-5x+7)(2x2-3x+1).
FirstInnerProduct ofFirstTermsProduct ofLastTermsOuterLastProduct ofOuterTermsProduct ofInnerTermsSpecial ProductsThe method outlined for multiplying polynomials works forallproducts of polynomials. Forthe special case when both polynomials are binomials, theFOIL methodcan also be used.WORDSMATHApply the distributive property.(5x1)(2x3)5x(2x3)1(2x3)Apply the distributive property.5x(2x)5x(3)1(2x)1(3)Multiply each set of monomials.10x215x2x3Combine like terms.10x213x3The FOIL method finds theproducts of theFirst terms,Outer terms,Inner terms, and(5x1)(2x3)10x215x2x3Last terms.EXAMPLE 6Multiplying Binomials Using the FOIL MethodMultiply (3x1)(2x5) using the FOIL method.Solution:Multiply thefirstterms.(3x)(2x)6x2Multiply theouterterms.(3x)(5)15xMultiply theinnerterms.(1)(2x)2xMultiply thelastterms.(1)(5)5Add the first, outer, inner, and last terms,and identify the like terms.Combine like terms.6x213x5YOUR TURNMultiply (2x3)(5x2).(3x+1)(2x-5)=6x2-15x+2x-5Answer:10x219x6Study TipWhen the binomials are of the form(axb)(cxd), the outer and innerterms will be like terms and can becombined.
EXAMPLE 7Multiplying Binomials Resulting in Special ProductsFind the following:a.(x5)(x5)b.(x5)2c.(x5)2Solution:a.(x-5)(x+5)=x2+5x-5x-52=x2-52=x2-2532CHAPTER 0Prerequisites and ReviewSquare of a binomial sum:(ab)2(ab)(ab)a22abb2Square of a binomial difference:(ab)2(ab)(ab)a22abb2PERFECT SQUARES(a+b)(a-b)=a2-b2DIFFERENCE OF TWO SQUARESEXAMPLE 8Finding the Square of a Binomial SumFind (x3)2.INCORRECTERROR:Don’t forget the middle term, which istwice the product of the two terms inthe binomial.(x+3)2Zx2+9CORRECT(x3)2(x3)(x3)x23x3x9x26x9Forgetting the middle term, which istwicethe product of the two terms inthe binomial.CO M M O NMI S TA K ELetaandbbe any real number, variable, or algebraic expression in the followingspecial products.Some products of binomials occur frequently in algebra and are given special names.Example 7 illustrates thedifference of two squaresandperfect squares.rFirstrInnersDifference of two squaresrOuterrLastrFirstrInnerrOuterrFirstrInnerrOuterrLastrLastb.

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