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Algebra Cheat Sheet
Basic Properties & Facts
Arithmetic Operations ab + ac = a ( b + c ) a   a b = c bc a c ad + bc + = b d bd a −b b−a = c−d d −c ab + ac = b + c, a ≠ 0 a Exponent Properties a n a m = a n+m an 1 = a n−m = m−n m a a a 0 = 1, a ≠ 0 a a   = n b b 1 = an −n a
n n n

 b  ab a  = c c a ac = b b   c a c ad − bc − = b d bd a+b a b = + c c c a   ad b =  c  bc   d

Properties of Inequalities If a < b then a + c < b + c and a − c < b − c a b If a < b and c > 0 then ac < bc and < c c a b If a < b and c < 0 then ac > bc and > c c Properties of Absolute Value if a ≥ 0 a a = if a < 0  −a a ≥0 −a = a ab = a b a+b ≤ a + b a a = b b Triangle Inequality

Distance Formula If P = ( x1 , y1 ) and P2 = ( x2 , y2 ) are two 1 points the distance between them is d ( P , P2 ) = 1

(a )

n m

= a nm = a nb n 1 an bn b =  = n a a

( x2 − x1 ) + ( y2 − y1 )
2

2

( ab )

n

Complex Numbers i = −1
n
1 m

a −n = a   b
−n

i 2 = −1

−a = i a , a ≥ 0

a = a

n m

( ) = (a )
1 m

n

Properties of Radicals
n

( a + bi ) + ( c + di ) = a + c + ( b + d ) i ( a + bi ) − ( c + di ) = a − c + ( b − d ) i ( a + bi )( c + di ) = ac − bd + ( ad + bc ) i ( a + bi )( a − bi ) = a 2 + b 2
a + bi = a 2 + b 2 Complex Modulus

a = an a = nm a

1

n

ab = n a n b a na = b nb

m n

n

n n

a n = a, if n is odd a n = a , if n is even

( a + bi ) = a − bi Complex Conjugate 2 ( a + bi )( a + bi ) = a + bi

For a complete set of online Algebra notes visit http://tutorial.math.lamar.edu.

© 2005 Paul Dawkins

Logarithms and Log Properties Definition y = log b x is equivalent to x = b y Example log 5 125 = 3 because 53 = 125 Special Logarithms ln x = log e x natural log log x = log10 x common log where e = 2.718281828K Factoring Formulas x 2 − a 2 = ( x + a )( x − a ) x 2 + 2ax + a 2 = ( x + a ) x 2 − 2ax + a 2 = ( x − a )
2 2

Logarithm Properties log b b = 1 log b 1 = 0 log b...

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<http://trenmayamx.com/free-essays/Miss-191113.html>

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Miss. Anti Essays. Retrieved December 18, 2018, from the World Wide Web: http://trenmayamx.com/free-essays/Miss-191113.html