| A | B |
|---|
| Property | a fact that is true concerning that system |
| Axiom | a property that forms the basis of a mathematical system. Its is assumed to be true without proof |
| Distributive axiom | x(y+z) = xy + xz |
| Multiplication distributes over subtraction | x(y - z) = xy - xz |
| Distributing | Multiplication or division distrbute over addition or subtraction of 2 or more terms from left to right. |
| Like Terms | 2 terms in an expression that have the same variables raised to the same powers |
| Numerical coefficient | The constant that is multiplied by the variables ( 5 in 5xy) |
| Common factor | 4 in 4x = 4y or 3 in 3x + 6y |
| Commutative axiom of addition | x + y = y + x |
| Commutative axiom of multiplication | xy = yx |
| associative axiom for addition | (x + y) + z = x + (y +z) |
| associative axiom of multiplication | (xy)z = x(yz) |
| distributive axiom for multiplication over addition | x (y+z) = xy = xz |
| additive identity axiom | x + 0 = x |
| multiplicative identity axiom | x (1) = x |
| additive inverse axiom | x + (-x) = 0 |
| multiplication inverses axiom | x (1/x) = 1 |
| multiplication property of -1 | -1 (x) = -x |
| multiplication property of zero | x * 0 = x |
| transitive axiom of equality | if x = y and y = z, then x = z |
| symmetric axiom of equality | if x = y , then y = x |
| reflexive axiom of equality | x=x |
| addition property of equalilty | If x + y, then x+ z = y + z |
| multiplicative property of equality | If x = y, then xz = yz |
