Algebraic Expressions and Identities - Fundamental Concepts

Vocabulary flashcards covering basic definitions, algebraic variables, constants, and fundamental operational laws.

Constant

A symbol which has a fixed value.

Variable

A symbol which can be given various numerical values; also called a literal.

Commutative Law (Addition)

The property of addition for any variables $x$ and $y$ stating that $x + y = y + x$.

Associative Law (Addition)

The property of addition for any variables $x$, $y$, and $z$ stating that $(x + y) + z = x + (y + z)$.

Additive Identity

The property stating that for any variable $x$, $x + 0 = x = 0 + x$.

Additive Inverse

The property stating that for any variable $x$, $x + (-x) = 0 = (-x) + x$.

Commutative Law (Multiplication)

The property of multiplication for any variables $x$ and $y$ stating that $xy = yx$.

Associative Law (Multiplication)

The property of multiplication for any variables $x$, $y$, and $z$ stating that $(xy)z = x(yz)$.

Multiplicative Identity

The property stating that for any variable $x$, $1x = x = x1$.

Distributive Law

The property stating that for any variables $x$, $y$, and $z$, $x(y + z) = xy + xz$ and $(y + z)x = yx + zx$.