The first step in learning Algebra is learning the definitions of the most commonly used words.
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’s only a phrase, not the whole sentence, so it doesn’t include an equal sign.
Here’s an example of an algebraic expression:
2x2 + 3xy – 4
In Algebra, the term equation means a statement of equality. It is a sentence in which two expressions are placed equal to one another. In order to satisfy an equation, it is important to determine the value of the variable concerned; this is known as solution or root of the equation.
Here are some examples of algebraic equations:
2x2 – 3x = 12
3x + 13 = 8x – 2
5x + 3y = 7
In an algebraic expression, terms are the elements separated by the plus or minus signs. The algebraic expression 2×2 + 3xy – 4 has three terms: 2x2, 3xy, and 4. Terms may consist of variables and coefficients, or constants.
In algebraic expressions, letters represent variables. These letters are actually numbers in disguise. In this expression, the variables are x and y. We call these letters “variables” because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression.
Coefficients are the number part of the terms with variables. In the expression 2x2 + 3xy – 4, the coefficient of the first term is 2 and the coefficient of the second term is 3.
If a term consists of only variables, its coefficient is 1.
Constants are the terms in the algebraic expression that contain only numbers. That is, they’re the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value. In the expression 2x2 + 3xy – 4 the constant term is “4.”
Expression vs. Equation
A lot of people are often confused with expressions and equations, as they are used in Algebra. Sometimes these two related but very different words are even used interchangeably by some people.
The easiest and fastest way to identify whether a given problem is an expression or equation is presence or absence of an equal sign (=).
If an equal sign is present, then it most definitely is an equation.
If there is no equal sign, then it most likely an expression.