IMPORTANT ALGEBRA FORMULAS AND THEOREMS

 

Quadratic Formula

If ax2 + bx + c = 0, then x = (-b + sqrt(b2 – 4ac))/2a.

(where a, b, c are constants & a not equal to 0)

 

Exponents and Radicals

axay = ax + y                                 a1/x = x√a

(ax)y  = axy                                 ax/y = y√ax

(ab)x = axbx                                               ax/y = ( y√a)x

(a/b)x = ax/bx                                          x√ab = x√a x√b

ax/ay = ax-y                                 x√(a/b) = x√a/x√b

a-x = 1/ax                                                    x√y√a = xy√a

 

Absolute Value

|x| < a   if and only if   -a<x<a

|x| > a   if and only if either x>a or x<-a

 

Special Product Formulas

(x + y)(x – y) = x2 – y2

(x + y) 2 = x2 + 2xy + y2               (x – y) 2 = x2 – 2xy + y2

(x + y)3 = x3 + 3xy2 + 3xy2 + y3    (x – y) 3 = x3 – 3xy2 + 3xy2 – y3

 

Binomial Theorem

(x + y)n = x n + (n1)x n-1 y + (n2)x n-2 y 2 + ... + (nk)x n-k y k + ... + y n,

where (nk) = n!/k!(n – k)!

 

Special Factoring Formulas

X2 – y2 = (x + y)(x – y)

x2 + 2xy + y2 = (x + y)2                        x2 – 2xy + y2 = (x – y) 2

x3 – y3 = (x – y)(x2 + xy + y2)               x3 + y3 = (x + y)(x2 – xy + y2)

 

Inequalities

If a>b and b>c, then a>c.

If a>b, then a+c>b+c.

If a>b and c>0, then ac>bc.

If a>b and c<0, then ac<bc.

 

Exponentials and Logarithms

y = logax  ó ay = x                     logaxy = logax + logay

loga (x/y) = logax – logay              logaxr = rlogax

alogax = x                                    logaax = x

loga1 = 0                                    logaa = 1

logx = log10x                              lnx = logex

logbu = logau/logab