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This lesson will explain how to recognize a mathematical expression and the parts that make up a mathematical expression. 

A problem as simple as 12 + 2 is a mathematical expression. 

Addition, subtraction, multiplication, and division are called operations. 

Variables in Mathematical Expressions:

In algebra, variables or letters are used to represent numbers. 
An example of a mathematical expression with a variable is 2x + 3. 

All variables must have a coefficient, a number that is multiplied by the variable. 
In the expression 2x + 3, the coefficient of x is the number 2, and it means 2 times x plus 3. 

Since x is often used as a variable, in algebra the symbol x is rarely used to show multiplication. Sometimes a dot, an asterisk, or parentheses may be used instead. 
For example, 2x + 3 could also be expressed as 2(x) + 3 or 2 * x + 3.

What is the coefficient of x in an expression like x + 4? 
Anytime you don't see the coefficient, a 1 is implied to be there. So, the coefficient of x is understood to be the number 1. 

Sometimes, operations are applied directly to a variable in mathematical expressions. For example, in the expression 3x^2, the squaring operation is being applied to the variable x. In the expression 2 * square root y, the square root operation is being applied to the variable y. In these cases, we would say 3x^2 has a coefficient of 3, or 2 * square root y has a coefficient of 2.

Mathematical expressions may be multivariate, which means they have more than one variable. An example of a multivariate expression is 4xy - 5x + 7. Just as 2x means 2 times x, 4xy means 4 times x times y.

Variables may also be in the denominator of a fraction, as in the expression 7x/y. 

All mathematical expressions contain parts called terms. The term of a mathematical expression is separated from other terms with either plus or minus signs and consist of the product a coefficient and one or more variables. A single term may contain an expression in parentheses or other grouping symbols. In this case, the grouped expression is part of that term. For example, -2x/(x + 1) is considered 1 term, with a coefficient of -2. 



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