## What are Like and Unlike Terms: Introduction

## FAQs on Difference Between Like and Unlike Terms

1. Can like terms have different exponents?

No, like terms cannot have different exponents. In mathematics, like terms are defined as algebraic terms that have the same variables raised to the same powers. The exponents indicate the power to which the variable is raised. For terms to be considered like terms, they must have the exact same exponents attached to their variables. For example, 3x² and 5x² are like terms because they both have the variable x raised to the power 2. However, 3x² and 5x³ are unlike terms because they have different exponents (2 and 3, respectively) attached to the variable x.

2. Can you add or subtract, unlike terms?

No, unlike terms cannot be directly added or subtracted. Unlike terms have either different variables or the same variable raised to different powers. Since they lack the necessary common factors to combine algebraically, addition or subtraction is not possible without further manipulation. To perform operations involving unlike terms, one must first simplify or rearrange the expressions by factoring out any common factors or by using other algebraic techniques. Once the expressions are simplified and like terms are identified, addition or subtraction can be performed on the like terms to obtain the desired result.

3. What are the properties of like terms?

Firstly, like terms have identical variables, meaning they contain the same letter or symbol representing the variable. Secondly, like terms possess the same exponents attached to their variables. This implies that the variables are raised to the same power. Thirdly, the coefficients of like terms can be added or subtracted while keeping the variables and exponents unchanged. This property allows for the combination and simplification of like terms. By grouping together like terms, algebraic expressions can be condensed and manipulated more effectively.

4. Can variables in like terms have different letters?

No, variables in like terms cannot have different letters. Like terms are characterised by having the same variables, meaning they must use the exact same letter or symbol to represent the variable. For example, 3x and 5y are not like terms because they have different variables, x and y, respectively. In like terms, the variables must be identical, ensuring that they represent the same quantity or unknown value. Having different letters would imply different variables and, therefore, such terms would not meet the criteria to be considered like terms.

5. Can constant terms be considered like terms?

Yes, constant terms can be considered like terms. Like terms are not limited to variables alone, but they can also include constant terms. Constant terms are those that do not contain any variables. Since they lack variables, their exponents are considered to be zero. When two constant terms have the same numerical value, they can be regarded as like terms. For example, 3 and -3 are like terms because they are both constant terms with a value of 3, albeit with different signs. Like terms with constant terms can be combined by adding or subtracting their coefficients to simplify expressions and perform arithmetic operations.