Calculus I

Algebra Fact Sheet

Basic Algebra

( )2 2 22a b a ab b+ = + +

( )3 3 2 2 33 3a b a a b ab b+ = + + +

( )( )2 2a b a b a b = + ( )( )2 2a b a bi a bi+ = +

( )( )3 3 2 2a b a b a ab b = + + ( )( )3 3 2 2a b a b a ab b+ = + +

a c ad bcb d bd

=

Rules of Exponents m n m nx x x +=

mm n

n

x xx

=

( )nm mnx x= / nm n mx x=

1nnx x

=

1x yy x

=

( )0 1 0x x=

Radicals 1/2x x= 1/33 x x=

Real Numbers xy x y=

x xy y=

Complex Numbers 1i =

2 1i =

Logarithmic Functions

log yby x b x= =

( )log log logb b bmn m n= +

log log logb b bm m nn

=

log lognb bm n m= 1log logb b xx

=

log xb b x= logb xb x=

Quadratic Formula/Solving 2 0ax bx c+ + =

2 42

b b acxa

=

2x n x n= =

Natural and Common Logarithms

( )10

log ln 2.71828log log

e x x ex x=

=

ln yy x e x= = log 10yy x x= =

ln xe x= ln 1e = ln xe x= ln1 0=

log log lnloglog log ln

ba

b

x x xxa a a

= = =

Graphs of Exponentials and Logs

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