Literal: The letters used to represent numbers are called literal numbers or literals.

Variable: In algebra, the letter that stands for an unknown number is called a variable. The variables in 8x²y³ are x and y.

Numeric Co-efficient: The number that multiplies a variable or variables is called a coefficient. It is usually written in front of the variable or variables. The coefficient in 9yz⁴ is 9. When the coefficient is 1, it is typically not written (i.e., 1yz⁴ = yz⁴ and 1a³ = a³).

Exponent/Index and Base: The power to which a variable is raised is called an exponent. The number or variable that is multiplied by itself is called the base. In 7a⁵, the exponent is 5 and the base is a. When the exponent is 1, it is typically not written (i.e., 6y¹z⁴ = 6yz⁴).

Any variable or a number raised to the power zero gives one (i.e., x⁰ = 1).

Term: A term is a number, variable, or the product of a number and variable(s). Examples of terms are 3x, 4x³, 7xy, x.

Like Terms are terms that have the exact same variables raised to the exact same exponents.
Examples of like terms: 5x² and -6x²; 8ab³ and 9ab³

Algebraic Expression: An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It is only a phrase, not the whole sentence, so it doesn't include an equal sign.
Example: 2x² + 4y + 8xy + 15

In an algebraic expression, terms are the elements separated by plus or minus signs. The above example has four terms, 2x², 4y, 8xy, and 15. Terms may consist of variables and coefficients, or constants.

Algebraic Equation: An equation is a statement that two numbers or expressions are equal.
Example: x + 5 = 12 - x

Algebraic Inequalities: An algebraic inequality is a mathematical statement comparing two unequal algebraic expressions. It states that one algebraic expression is greater than (>), less than (<), greater than or equal to (>=), or less than or equal to (<=) another algebraic expression.

Monomial: Any number or a variable or a product of numbers and variables is called a monomial. Each of the following is an example of a monomial:
5, -7, x, y, 6xyz, -9yz⁴, 2.3a³

Polynomial: An expression containing a finite sum of terms.
Examples of Polynomials:
9x; x²+ 4x = 3

The following are NOT Polynomials:
6x^-2 because of the negative exponent, the expression is 1/x² has the variable in the denominator;
sqrt(x) - this has a variable inside a radical

Binomial: A polynomial with two terms.
Example: 4x² - 2x + 7

Trinomial: A polynomial with three terms.
Example: 3x³ + 4x² - 2x + 7

Degree of a Term: The degree of a term is the sum of the exponents on the variables contained in the term. For example, the degree of the term 4x² is 2.

Degree of a Polynomial: The degree of a polynomial is the largest degree of all its terms.
Examples:
The degree of 4x² - 2x + 7 is 2.
The degree of 3x³ + 4x² - 2x + 7 is 3.