Simplifying an expression: like terms

What is a like term?

Two terms are like (or, as we say, ‘of the same kind’) if they contain exactly the same letter raised to the same power. We can then add or subtract them to simplify the expression, that is, to write it with as few terms as possible.

Example: 3x and 5x are like terms, so 3x + 5x = 8x (we add the coefficients: 3 + 5 = 8).

Examples of simplification

Original expression	Simplified expression
3x + 5x	8x
7x - 2x	5x
4x + 3y	4x + 3y (cannot be simplified)
2x² + 5x²	7x²
6x + 2 + 3x - 1	9x + 1

To simplify an expression with several terms, first group like terms together, then add them up.

Example: H = 6x + 2 + 3x - 1 We group them together: H = (6x + 3x) + (2 - 1) = 9x + 1

Common pitfall

2x and 2x² are not like terms! The first contains x, the second contains x² (i.e. x times x). We cannot add them together to make 4x² or 4x. Similarly, 3x and 3y are not like terms because they involve different letters: 3x + 3y remains 3x + 3y; we cannot simplify it any further.