In algebra, variables are symbols used to represent unspecified numbers or values.

An algebraic expression consists of one or more numbers and variables along with one or more arithmetic operations.

In an expression, the quantities being multiplied are called factors.
Example: 5 * 7 = 35

The 5 and the 7 are called factors and the 35 is called the product.

The result (answer) of multiplication.
Example: 3 * 4 = 12

The 3 and the 4 are called factors and the 12 (result) is called the product.

An expression like x^n is called a power and is read "x to the nth power".
The variable x is called the base, and n is called the exponent.

Example: 3^4

3 to the fourth power.

To evaluate an expression means to find its value.
Example: Evaluate 2^3

2^3 = 2 * 2 * 2

= 8

Numerical expressions often contain more than one operation. A rule is needed to let you know which operation to perform first. This rule is called the order of operations.

P - Parenthesis (all grouping symbols)
E - exponents
M - multiplication (from left to right)
D - division (from left to right)
A - addition (from left to right)
S - subtraction (from left to right)

The mneumonic "Please Excuse My Dear Aunt Sally" is often used to remember the order of operations.

A mathematical statement with one or more variables is called and open sentence. An open sentence in neither true nor false until the variables have been replaced by specific values.

The process of finding a value for a variable that results in a true sentence is called solving the open sentence.

The replacement value that makes an open sentence true is called the solution of the open sentence.

A sentence that contains an equals sign, = , is called an equation.

A set of numbers from which replacements for a variable may be chosen is called a replacement set.

A collection of objects or numbers.
It is often shown using brackets, \{ \quad \}, and is usually named by a capital letter.
Each object or number in the set is called an element.
Example:

A = \{ -2, -1, 0, 1, 2 \}

Each object or number in a set is called an element of the set.
Example: Set A = \{ -2, -1, 0, 1, 2 \}

Each number -2, -1, 0, 1, 2 is an element of Set A.

The solution set of an open sentence is the set of elements from the replacement set that make an open sentence true.

An open sentence that contains the symbol < , \leq , > , or \geq is called an inequality.
Inequalities can be solved in the same way as equations.

The sum of any number and 0 is equal to the number.
Thus, 0 is called the additive identity.

Example: 5 + 0 = 5, \quad 0 + 5 = 5

The product of any number and 1 is equal to the number.
Thus, 1 is called the multiplicative identity.

Example: 7 * 1 = 7, \quad 1 * 7 = 7

Two numbers whose product is 1 are called multiplicative inverses or reciprocals.

Example: 3 * \frac{1}{3} = 1
The numbers 3 and \frac{1}{3} are multiplicative inverses of one another.

A term is a number, a variable, or a product or quotient of numbers and variables.
Terms can also be thought of as "things being added."

Example: \quad y, p^3, 4a, \quad and 5g^2h are all terms.

Like terms are terms that contain the same variables, with corresponding variables having the same power.

Example:

\quad 3a^2 \quad 5a^2 \quad are like terms.

\quad 6a \quad 8a \quad are like terms.

\quad 2a \quad 7a^2 \quad are NOT like terms.

\quad 3b \quad 5a \quad are NOT like terms.