Algebraic expressions are a combination of variables, coefficients, constants separated by operations(\(+, -, \times, \div\)). Operations on algebraic expressions can be performed only on like terms.
Like terms
Terms having same variables are called as like terms.
Example:
- \(3x\) and \(2x\) are like terms. [Having same variable \(x\)]
- \(16ab\) and \(2ab\) are like terms. [Having same variable \(ab\)]
- \(7y + 3 + 5y + 1\). [Here \(7y\) and \(5y\) are like terms because of variable \(y\) and \(3\) and \(1\) are constants]
Unlike terms
Terms having different variables are called as unlike terms.
Example:
- \(5x\) and \(8y\) are unlike terms. [Having different variables \(x\) and \(y\)]
- \(3xy\) and \(12y\) are unlike terms [Having different variables \(xy\) and \(y\)]
These cannot be combined.
Addition and Subtraction of expressions
To add or subtract the expressions:
1. Identify the like terms.
2. Add/Subtract the coefficients of like terms.
Example 1: Add the expression \(2x + 7x\)
Here, \(2x\) and \(7x\) are like terms. To add the expression, let us add its coefficients.
\(2x + 7x = (2 + 7)x\)
\(= 9x\)
Example 2: Subtract the expression \(7xy - 15xy\)
Here, \(7xy\) and \(15xy\) are like terms.
\(7xy - 15xy = (7 - 15)xy\)
\(= -8xy\)
Example 3: Simplify the expression \((12ab + 5d) - (4ab - 7d)\)
Let us combine the like terms.
\((12ab + 5d) - (4ab - 7d) = 12ab + 5d - 4ab + 7d\)
\(= (12 - 4)ab + (5 + 7)d\)
\(= 8ab + 12d\)
Therefore, the expression is simplified into \(8ab + 12d\).