Transcription of Algebra Cheat Sheet - Lamar University
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Algebra Cheat Sheet - Lamar University
For a complete set of online Algebra notes visit 2005 Paul Dawkins Algebra Cheat Sheet Basic Properties & Facts Arithmetic Operations (),0bababacabcaccaaaacbbcbcbcacadbcacadb cbdbdbdbdabbaababcddccccaabacadbbcacabcd +=+= == +-+=-=--+==+-- + =+ = Exponent Properties ()()()()11011, 011nmmmnnmnmnmmmnmnnmnnnnnnnnnnnnnnnnaaa aaaaaaaaaaababbbaaaaabbaaabaa+-----===== == == ==== Properties of Radicals 1,if is odd,if is evennnnnnnmnnmnnnnnnaaababaaaabbaanaan== ==== Properties of Inequalities If thenand If and 0 then and If and 0 then and abacbcacbcababcacbcccababcacbccc<+<+-<-<> <<<<>> Properties of Absolute Value if 0if 0aaaaa = -< 0 Triangle Inequalityaaaaaababbbabab -===+ + Distance Formula If ()111,Pxy= and ()222,Pxy= are two points the distance between them is ()()()22122121,dPPxxyy=-+- Complex Numbers ()()()()()()()()()()()()()()22222211,0 Complex ModulusComplex Conjugateiiaiaaabicdiacbdiabicdiacbdiabicdiacbdadbciabiabiababiababiabiabiabiabi=-=--= +++=++++-+=-+-++=-+++-=++=++=-++=+ For a complete set of online Algebra notes visit 2005 Paul Dawkins Logarithms and Log Properties Definition log is equivalent to ybyxxb== Example 35log1253 because 5125== Special Logarithms 10lnlognatural logloglogcommon logexxxx== where Logarithm Properties ()()loglog1log10logloglogloglogloglogloglogbbbxxbrbbbbbbbbbbxbxxrxxyxyxxyy======+ =- The domain of logbx is 0x> Factoring and Solving Factoring
(1) ( )1 0 1 1, 0 11 n mmm n nmnmnm mmn nm nm n n n nn n nn nn nnn n n n a aaaa aa aaaa aa abab bb aa aa abb aaa baa +-----=== ==„ æö ==ç÷ Łł == æöæö ç÷=ç÷=== ŁłŁł Properties of Radicals 1,if is odd,if is even nn nnn n mnnm n n nn nn aaabab aa aa bb aan aan == == = = Properties of Inequalities If thenand If and 0 then and If ...
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