Algebraic expression is a set of constants, variables and operators with or without combinations, algebraic expressions can be in different forms.
1 An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). 2  Here are some algebraic expressions: 3  a + 1. 4  a-b. 5  3x. 1 Algebraic Expression. 2  An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). 3  Here are some algebraic expressions: 4  a + 1. 5  a-b. 6  3x. 7  x-a / b. 8  In the above expression the / means divide An algebraic equation is an equation that includes one or more variables. Any expression that contains letters, numbers and algebraic operations, addition(+), subtraction(-), multiplication(×), division(÷) and exponentiation to rational exponent is called an Algebraic Expression. While studying the algebraic expression first question arises in our mind, what is an algebraic expression. Algebraic expression is a set of constants, variables and operators with or without combinations, algebraic expressions can be in different forms. $3x + 4y + z$ is an Algebraic expression. 3x, 4y, z are the terms of the Algebraic expression. All these terms are separated by (+) sign. $3x^{2} - 2x +7$ is also an Algebraic expression. The terms $3x^{2}$ and $2x$ are separated by (-) sign and not (+) sign. We can rewrite the same expression as $3x^{2} + (-2x) +7$. $3x^{2}$ and $-2x$ are variable terms and 7 is a constant term. Observe that -2x is a term and not 2x.  Summary: A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change. An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.  An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.  Note: An expression is just a mathematical phrase. In this tutorial, you'll learn about two popular types of expressions: numerical and algebraic expressions. A numerical expression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables. For the notion in formal languages, see regular expression. In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). The roots of a polynomial expression of degree n, or equivalently the solutions of a polynomial equation, can always be written as algebraic expressions if n quadratic formula, cubic function, and quartic equation). Such a solution of an equation is called an algebraic solution. In mathematics, an expression (or mathematical expression) is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, punctuation, grouping, and other aspects of logical syntax. 
http://home.avvanta.com/~math/def2.cgi?t=expression http://www.algebraicexpression.org/ http://www.mathcaptain.com/algebra/algebraic-expressions.html http://www.mathgoodies.com/lessons/vol7/expressions.html http://www.mathgoodies.com/glossary/term.asp?term=algebraic%20expression http://www.virtualnerd.com/middle-math/number-algebraic-sense/variables-expressions/numerical-algebraic-expressions https://en.wikipedia.org/wiki/Algebraic_expression https://en.wikipedia.org/wiki/Expression_(mathematics)
what is an algebraic expression