Transcription of REVIEW OF ALGEBRA - Stewart Calculus
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REVIEW OF ALGEBRA - Stewart Calculus
REVIEW OF ALGEBRAHere we REVIEW the basic rules and procedures of ALGEBRA that you need to know in orderto be successful in OPERATIONSThe real numbers have the following properties:(Commutative Law)(Associative Law)( distributive law)In particular, putting in the distributive Law, we getand soEXAMPLE 1(a)(b)(c)If we use the distributive Law three times, we getThis says that we multiply two factors by multiplying each term in one factor by each termin the other factor and adding the products. Schematically, we haveIn the case where and , we haveor Similarly, we obtainEXAMPLE 2(a)(b)(c) 12x2 5x 21 12x2 3x 9 2x 123 x 1 4x 3 2 x 6 3 4x2 x 3 2x 12 x 6 2 x2 12x 36 2x 1 3x 5 6x2 3x 10x 5 6x2 7x 5 a b 2 a2 2ab b22 a b 2 a2 2ab b21 a b 2 a2 ba ab b2d bc a a b c d a b c d a b c a b d ac bc ad bd4 3 x 2 4 3x 6 10 3x2t 7x 2tx 11 14tx 4t2x 22t 3xy 4x 3 4 x2y 12x2y b c b c b c 1 b c 1 b 1 ca 1a b c ab ac ab c a bc a b c a b c ab baa b b a1 Stewart : Calculus ,Sixth Edition.
(d) FACTORING We have used the Distributive Law to expand certain algebraic expressions. We sometimes need to reverse this process (again using the Distributive Law) by factoring an expression
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