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Understanding Algebraic Expressions

Understanding Algebraic Expressions

Expressions that contain only constants are called numeric or arithmetic expressions.

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Expressions that contain only constants are called numeric or arithmetic expressions.
Eg:
Expressions that contain constants and variables, or just variables, are called algebraic expressions.
Eg:,
While writing algebraic expressions, we do not write the sign of multiplication.  An algebraic expression containing only variables also has the constant 1 associated with it.  The parts of an algebraic expression joined together by plus (+) signs are called its terms
For example, the number of terms in the expression  is 3.
A term that contains variables is called a variable term

A term that contains only a number is called a constant term.  The constants and the variables whose product makes a term of an algebraic expression, are called the factors of the term.  The factors of a constant term in an algebraic expression are not considered.  The numerical factor of a variable term is called its coefficient.  The variable factors of a term are called its algebraic factors.

Terms that have different algebraic factors are called unlike terms.  Terms that have the same algebraic factors are called like terms.  Algebraic expressions that contain only one term are called monomials.  Algebraic expressions that contain only two unlike terms are called binomials.  Algebraic expressions that contain only three unlike terms are called trinomials.  All algebraic expressions that have one or more terms are called polynomials. Therefore, binomials and trinomials are also polynomials.