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).
Get answer to your question and much more
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.6x213x5■YOUR TURNMultiply (2x3)(5x2).(3x+1)(2x-5)=6x2-15x+2x-5■Answer:10x219x6Study TipWhen the binomials are of the form(axb)(cxd), the outer and innerterms will be like terms and can becombined.