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 Conjugateiiaiaaabicdiacbdiabicdiacbdiabi cdiacbdadbciabiabiababiababiabiabiabiabi =-=--= +++=++++-+=-+-++=-+++-=++=++=-++=+ 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

Absolute Value Equations/Inequalities If b is a positive number or or pbpbpb pbbpb pbpbpb =Þ=-= <Þ-<< >Þ<-> Completing the Square Solve 2xx2-6-=100 (1) Divide by the coefficient of the x2 xx2-3-=50 (2) Move the constant to the other side. xx2-=35 (3) Take half the coefficient of x, square it and add it to both sides 22 233929 355 2244 xx ...

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  University, Value, Inequalities, Absolute, Lamar university, Lamar, Absolute value

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