Algebra Cheatsheet

Laws of Exponents & Radicals Factoriall l a , be R ,a ,b>0 ,and p ,e , t , sa ree Q , then :

1. e 'x*=a ' " } # =n+e-r u . (A '=ff to* ot

(a+ 0)

7. r=J- (a* 0)ar

a a - t b

$. 6;=-r/6r ai =,la

Binomial Theorem

2 . t = a ' - "as

3. (afs = ars

a. @blr = dU

6 . d = 1

n! = n (n-1) (n-2) . . . (2) (1)

5! = 5 (4) (3) (2) (1)

Factoring2 3 -

2 3 = \ * * - e = ( a + b l ( a - b l

* + Z a b + 8 = ( a + 6 7 2

d + F = ( a + b ) ( * - a b + E l

db - ab= ab (a + 1 ) ( a - 1 )

* - 2 a b + B = ( a - 6 7 2

a 3 - 6 e = ( a - b l ( * + a b + 8 1

(x+h,=n+( I ) * - , , .(f) )e- 2f

. (oJ* -kf * ...+ f,

nrtrere(*o)= ffi

Absolute Value (d > 0)l r l . a i f and only i f 4 < x < d

l*1, a if and only if either x> d or x < 4

l a+b l< l a l+ l o l- l " l <a< la l

lnequalities

Binomial Expansion

a (b+ C l= ab+ ac

(a+ b l (c+ d)= ac+ ad+ bc+ bd

( a + b Y z = * + 2 a b + E

( a - P Y z = f i - 2 a b + 8

( a + 6 1 s = a 3 + 3 * b + 3 a 8 + 6

@ - n y t = f i - 3 4 b + 3 a 8 - F

(a + O7+ = d + 4*b + 6*E + 4# + 6

(a+ 61s = d + Sdb + l0a3e + 1O*6 + 5afa + F

(*- *l - (x+ al (x- al

(x8- a3) = (x- al (* + ax+ *l

(.xs + as) = (x+ a) (*- att+ *)

Algebra

Soarces:Geometry Glossaryhttp//library.think0uest.o19/2647/9eometry/glossary.htm

Wright, John W. ed. The New York TTmesAlmanac Millennium Edition.Penguin Reference

Algebraic ldentitieshtF /Awvw.sosmath.corVtableValg iden/alg iden.html

Algebra PostulateshttB:/Amrw.education-world.com/math/oost algebn.shtml

Swokowski, 0fnik and Perrce. Cabqlus of a Single Vaiable, 2nd EditionP.W.S.

l f a > b a n d b > c , t h e n a > c

lf a > b, then a+c > b+c

lf a > b ard c > 0, then ac > bc

lf a > b and c < 0, then ac < bc

Quadratic Formula

ff a * 0, the roots of a* + bx + c = 0 are

_bt{Ercc

Logarithms

2a

)r = fOg, X means dl = X

lo€try = log" x+lq"y

,*"i= bg" x- l9g^y

fog".rr= rlog"x

l o g r l = 0

l o g r a = 1

log x- loglex

ln x= log"x