1. Meaning of Algebraic Expressions
Before we understand the meaning of expressions, let us know about variables and terms.
A variable is an unknown number represented by letters a, b, x, y etc. A term is a combination of variables and numbers. For example, 12x, 9, x, 12yz etc.
(Note: Only numbers or only variables are also called terms.)
Terms separated by arithmetic operations (+, -, , ) are known as expressions. For example, 10a - 16b
1.1 Simplifying Expressions by Collecting Like terms
Simplifying expressions means writing them in the simplest form possible. To simplify expressions, we need to know about like terms.
Like terms are terms with the same letters and indices, while unlike terms have different letters or indices.
Examples of like terms are 11y, 10y or 8a², 11a² etc.
Examples of unlike terms are p, pq or n, n² etc.
To simplify an algebraic expression, add or subtract only the like terms.
For example let us try to simplify 2x + 12x - 7y - 2y.
First, identify the like terms in the expression. Here 2x and 12x are like terms while 7y and 2y are like terms.
So add or subtract the like terms just like we add two numbers keeping in mind the signs in front of them. 2x + 12x = 14x and -7y - 2y = -9y. We can write it as 14x - 9y.
Since 14x and 9y are unlike terms, we cannot simplify further, and 14x - 9y is the answer.
1.2 Expanding Brackets and Simplifying Expressions
Sometimes an expression can contain brackets which need to be expanded before simplifying it. To expand a bracket, multiply the term outside the bracket with each of the terms inside the bracket.
For example consider the expression 2(y + 3) + 2y.
First, we expand the brackets, 2y + 23 + 2y
Note that we don’t write the ‘’ symbol between numbers or variables. So, 2y means 2y.
We get 2y + 6 + 2y. Now add the like terms, which gives 4y + 6.
1.3 Example Questions on Simplifying Expressions
Example: Simplify 2a + 3b - 4c + 10a - 4b + 6c
Solution: Writing like terms together, 2a + 10a + 3b - 4b - 4c + 6c
Add or subtract the like terms, 12a - b + 2c
Example: Expand and simplify 5(a + b) - a(3 + b)
Solution: Expanding brackets, 5a + 5b - a³ - ab
Rewrite without the ‘’ sign, 5a + 5b - 3a - ab
Add or subtract the like terms, 2a + 5b - ab
