Definitions

1. An algebraic expression is a collection of terms connected by the signs "+, −, ×, and ÷".
E.g. 1 The algebraic expression 3x + 4y + 5 has 3 terms: 3x, 4y and 5.
E.g. 2 The algebraic expression 9p + 7 has 2 terms: 9p and 7. 

2. In the term 3x, the numerical part 3 is called the coefficient of x. In other words, the constant that is attached in front of a variable or a group of variables is called the coefficient. 
E.g. In the term 4y, 4 is the coefficient of y. 

3. The algebraic term that does not have a variable attached to it is called the constant term. 
E.g. In the expression 5x + 9, the constant term is 9. 

4. Algebraic terms that have the same variables where each variable has the same power are called like terms. They may differ in their coefficients. 

5. If two terms are not like terms, then they are called unlike terms. 

The table below shows some examples of like and unlike terms:

Addition and Subtraction of Linear Algebraic Expressions

Recall that only like terms can be added or subtracted. 

Things to note when removing brackets:
1. If the sign before the brackets is "+", then the signs remain the same when the brackets are removed.
E.g. 1 + (2a - 3b) = 1 + 2a - 3b

2. If the sign before the brackets is "-", then the signs need to be changed when the brackets are removed.
E.g. p - (5q - s) = 1 - 5q + s 

Simplifying Linear Algebraic Expressions 
1. When an algebraic expression contains brackets:
(a) Simplify the expression within the brackets first
(b) If the expression has more than one pair of brackets, simplify the innermost pair of brackets first.

2. The distributive laws of multiplication over addition and subtraction are given below. These laws will help us expand algebraic expressions.
a(x + y) = ax + ay
-a(x + y) = -ax - ay

Note:
If an expression inside the brackets is multiplied by a number or a variable, multiply each term inside the brackets by the number or the variable when the brackets are removed. The process of removing brackets and writing out the result term by term is called expansion of algebraic expressions.