Algebra - adding and subtracting

Algebra – Adding and Subtracting

Some students find the topic of algebra daunting when they meet it for the first time, but it needn’t be if they know how to distinguish between like and unlike terms for the purpose of adding and subtracting in algebra.


What is algebra and how do we add and subtract algebraic terms?

Algebra is a topic in mathematics in which letters and other symbols are used to represent numbers. In this blog, letter symbols are used to explain how we add and subtract algebraic terms.

Key points to remember when adding and subtracting algebraic terms.

  • A term contains a number, a letter symbol or a product of both. Example, 7, x and 7x are three terms. 7 is a number term, x is a letter term and 7x is a product of both.
  • A letter term without a number (coefficient) appearing before it means one lot of that letter term. In the example above, the term x can be written as 1x.
  • An expression is a collection of terms with at least one operation. Example, 2x + 3 is an expression. In this expression, we have a letter term 2x, a number term 3 and an operation of adding.
  • We can simplify an expression by adding and/or subtracting like terms.
  • Like terms are letter symbols of the same type. In the first example above, x and 7x are like terms because they both contain the same letter symbol x. Similarly, a2, -5a2 and 3a2 are like terms because they all contain the letter symbol a2.
  • We cannot add or subtract, unlike terms.
  • Unlike terms have different letter symbols or contain a letter symbol and a number. Example, 2x + 3 cannot be simplified by adding the terms together because they are unlike terms – one is a letter term and the other is a number term. Similarly, a, a2, and a3 are all unlike terms because they have different powers – they can’t be added or subtracted.


How do you simplify an expression?

You can start by rewriting the expression by collecting like terms. You simply write letters of the same type next to each other, then add or subtract them.