What is a term without a variable?

Algebraic expression started in the 9th century. In the beginning, it was more in statement form and not mathematical at all. For instance, algebraic equations used to be written as “5 times the thing added with 3 gives 18” which is basically 5x + 3 = 18. This type of equation which was not mathematical was Babylonian algebra. Algebra evolved with time and with the different forms provided. It started with Egyptian algebra, then came Babylonian algebra, then came greek geometrical algebra, moved to diophantine algebra, followed by Hindu algebra, then came Arabic algebra, and followed by abstract algebra. Today, the easiest and most convenient form of algebra is taught in classes for better understanding.

Algebraic Expressions

Algebraic expressions are the expressions obtained from the combination of variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and so on. An algebraic expression is made up of terms, there can be one or more than one term present in the equation. Let’s learn about the basic terms used in algebraic expressions,

Constants, Variables, Coefficients, and Terms

In the algebraic expression, fixed numerical are called constants, constants do not have any variables attached to them. For example, 3x – 1 has a constant -1 to it. Variables are the unknown values that are present in the algebraic expression, for instance, 4y + 5z has y and z as variables. Coefficients are the fixed values (real numbers) attached to the variables, they are multiplied with the variables. For example, 5x² + 3 has 5 as the coefficient of x². A term can be a constant, a variable, or a combination of both, basically, each term is separated by either addition or subtraction. For example, 3x + 5, 3x and 5 are the terms.

What is a term without a variable?

Answer:

A term can be a constant, a variable, or a combination of both. It is known that if the term does not have any variable, it will have only a constant. Therefore, it can be concluded that a term without a variable is a constant. For example, if a term is 5x, x is the variable, and 5 is the constant. Therefore, if x is removed from 5x, only 5 is remaining. Hence, only constant remains.

Sample Problems

Question 1: Find out the constant from the following algebraic expressions,

• 4x³ + 2x² – 9x + 3
• 13 + y⁵

Answer:

Constants are the terms that do not have any variable attached to them, therefore, in the first case, +3 is the constant, and in the second case, 13 is the constant.

Question 2: Find out the number of terms present in the following expressions,

• 7x² + 4x – 10
• 3y⁷ – 45

Answer:

Terms are separated by each other either by addition or subtraction sign. Therefore, in the first case, there are 3 terms and in the second case, there are 2 terms.

Question 3: Is 12 an algebraic expression?

Answer:

As it is clearly seen that 12 is a constant, even though, constants are a part of the algebraic expression, they do not complete the algebraic expression. For an expression to be an algebraic expression, a variable, and an operator is required as well. Variable can be any unknown term, for instance, x, y, z, etc. and, the operator can be +, -. Therefore, it is concluded that 12 is not an algebraic expression.