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Algebra Formulae & such

Factoring and Solving

x2 – a2 = (x+a)(x-a)

x2 + 2ax+ a2 =(x+a)

2

(x + a)2= x2 +2ax+ a2

x2 - 2ax + a2 = (x-a)2

(x-a)2= x2 - 2ax + a2

Arithmetic Operations

abc

a .

bc

abc

ac . b

Properties of

Inequalities

(adding or subtracting c)

If a < b then:

a+c < b+cand

a-c < b-c

(multiplying or dividing by c)

If a < b AND c > 0 then:

ac < bcand

a/c < b/c

(multiplying or dividing by c)

If a < b AND c < 0 then:

ac > bcand

a/c > b/c

Exponent Properties

(ab)n = anbn

(an)m = anm

anam = an+m

an/m = (a1/n)m

= (a1/m)n

a-n = 1 an

a0 = 1

a ≠ 0

(a/b)-n = (b/a)n

= bn

an

an/am = an-m

= 1/am-n

(a/b)n =

= an

bn

Properties of Radicals

ⁿ√a = a1/n

ⁿ√ab = ⁿ√a(ⁿ√b)

ⁿ√aⁿ = |a|

m√ⁿ√a =nm√a

n a/b =n√an√b