Algebra can be defined as a branch of mathematics that deals with the analysis or manipulation of mathematical symbols and integers. The subject basically deals with numbers theory, geometry, and analysis of problems with help of algebraic operations.
The given article explains various factors of terms, defines like and unlike terms with suitable examples, and solves the question that how to know if they are like or unlike terms.
Algebraic expressions are the expressions built up from the combination of terms which consists of integers, variables, coefficient, and algebraic operation.
Some terminologies of algebraic expressions
- Coefficient: Coefficients are the integers attached to the variable. For example, 4 is the coefficient of variable x in expression 4x+1.
- Variable: Variables are the unknown values of expression represented by alphabetical letters or symbols. For example, the letters like a, b, c, x, y, etc are the variables in an algebraic expression.
- Term: Term is a part of an expression that can be a variable or constant or coefficient attached to a variable.
Like terms are the terms having the same variable and exponent power. The like terms of an algebraic expression are simplified or combined to solve the expression. For example, if we have an expression
We will simplify this algebraic expression by combining the like terms.
Thus, the solution of the given expression is 3a2+ab+b2. As the terms, 2ab and ab had the same variables and exponent power which makes them like terms.
Unlike terms are the terms having different variable and exponent power. The unlike terms of an algebraic expression cannot be simplified or combined to solve the expression. For example, if we have an expression
The expression cannot be solved further as both the terms have different variables which makes them, unlike terms that cannot be combined.
How to identify like and unlike terms?
If the terms of an algebraic expression have the same variable with the same exponent power then, the terms are like terms. For example, we have two terms in an algebraic expression
Here, both the terms 6xy and 12xy have the same variable ‘xy’ and exponent power 1.
Hence, the terms can be combined together to get a solution.
Whereas, if the terms of an algebraic expression have different variables or exponent power then, the terms are unlike terms. For example, we have two terms in an algebraic expression
Here, one term has variable ‘x’ while the other one has variable ‘y’.
Question 1. Are 2x and 5xy like terms?
No, the given terms 2x and 5xy are unlike terms as both of them have different variables. The term 2x has variable ‘x’ and 5xy has variable ‘xy’.
Question 2. How do you identify like terms?
The terms in the expression having the same variable and exponent power are like terms.
Question 3. How do you solve like terms in an expression?
We can solve like terms in an expression with basic mathematical operations. The like terms can be added or subtracted as per the operation involved.
Question 4. Simplify: 9t3+17t-10t+3t2
Combining the like terms