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