Math Definitions, Axioms, and Properties
Factoring Out Polynomials
To factor out a polynomial is to transform it in tot he product of two or more factors.
Factoring Out Common Factors
xy+xz=x(y+z)
Axiom
A mathematical statement that is assumed to be true without proof.
Multiplication Property of -1
For any real number x(-1)=-x
Multiplication Property of 0
For any real number x(0)=0
Multiplicative Identity Axiom
For any real number x(1)=x
Multiplicative Inverses Axiom
For any real number x(1/x)=1
Distributive Axiom of Multiplication over Addition
For any real number x(y+z)=xy+xz
Associative Axiom of Multiplication
For any real number x(yz)=(xy)x
Additive Inverses Axiom
For any real number x+(-x)=0
Additive Identity Axiom
For any real number x+0=x
Commutative Axiom of Addition
For any real number x+y=y+x
Definition of Subtraction
For any real number x-y=x+(-y)
Definition of Division
For any real number x/y=x(1/y)
Associative Axiom of Addition
For any real number x=(y+z)=(x+y)+z
Reflexive Axiom of Equality
For any real number x=x
Commutative Axiom of Multiplication
For any real number xy=yx
Transitive Axiom of Equality
For any real number, if x=y and y=z then x=z
Subtraction Property of Equality (SPE)
For any real number, if x=y then x-z=y-z
Division Property of Equality (DPE)
For any real number, if x=y then x/z=y/z
Multiplication Property of Equality (MPE)
For any real number, if x=y then xz=yz
Symmetric Axiom of Equality
For any real number, if x=y then y=x
Addition Property of Equality (APE)
For any real number, if x=y, then x+z=y+z