Properties and Theorems CHARTS & TABLES
Properties and Theorems CHARTS & TABLES
Properties and Theorems (continued)
Axiom of Comparison
Only one of the following conditions can be true:
a<b,or
a=b,or
b<a
Binomial Square Theorem
(a+b)^2 =a^2 + 2ab+b^2
and
(a–b)^2 =a^2 – 2ab+b^2
Closure Property of Addition
a+bis a real number
Closure Property of Multiplication
abis a real number
Commutative Property of Addition
a+b=b+a
Commutative Property of Multiplication
ab=ba
Discriminate Theorem
If a, b,and care real numbers, and a≠0,
then ax^2 +bx+c= 0
has 0 real roots if b^2 – 4ac< 0
has 1 real root if b^2 – 4ac= 0
has 2 real roots if b^2 – 4ac> 0
Distributive Property of Multiplication over Addition
a(b+c) =ab+ac
and
(a+b)c=ac+bc
Distributive Property of Multiplication over Subtraction
a(b–c) =ab–ac
and
(a–b)c=ac–bc
Division of Real Numbers
If b≠ 0
a÷b=a×1/b
(continues)