A combination of variables, constants and operators constitute an algebraic expression. The four basic operations of mathematics viz. addition, subtraction, multiplication and division can also be performed on algebraic equations or expressions. Addition and subtraction of algebraic expressions is almost similar to addition and subtraction of numbers. But in case of algebraic expressions, like terms and the unlike terms must be sorted together.
The terms whose variables and their exponents are same are known as like terms and the terms having different variables are unlike terms.
Example: -5x2 + 12 xy – 3y + 7x2 + xy
In the given algebraic expression, -5x2 and 7x2 are like since both the terms have x2 as the common variable. Similarly, 12xy and xy are like terms.
The knowledge of like and unlike terms is crucial while studying addition and subtraction of algebraic expressions because the operation of addition and subtraction can only be performed on like terms.
Addition and subtraction of Algebraic Expressions:
- Addition of Algebraic expressions
For adding two or more algebraic expression the like terms of both the expressions are grouped together. The coefficients of like terms are added together using simple addition techniques and the variable which is common is retained as it is. The unlike terms are retained as it is and the result obtained is the addition of two or more algebraic expressions.
Example: Add 5xy – 3x2 – 12y +5x, xy – 3x – 12yz +5x3 and y – 6x2 – zy +5x3
Solution: For adding these three algebraic expressions the like terms are grouped together and added as shown below.
Arrange the terms of the given expressions in the same order.
- Subtraction of algebraic expressions:
For subtracting two or more algebraic expressions, it’s a better practice to write the expressions to be subtracted below the expression from which it is to be subtracted from. Like terms are placed below each other. The sign of each term which is to be subtracted is reversed and then the resulting expression is added normally.
Example:Subtract x2y –2x2 -zy + 5 and –3x2 +3x3 from y3 +3x2y –6x2 -6zy +7x3
Solution: The like terms of the expressions x2y – 2x2 – zy + 5 and – 3x2 + 3x3 are written below the like terms of the expression y3 +3x2y – 6x2 – 6zy + 7x3.
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