Simplifying Expressions

Collecting Like and Unlike Terms:

Like terms are terms whose variables (and their exponents such as the 2 in a²) are the same.

In other words, terms that are “like” each other. If they are not like terms, they are called, Unlike Terms.

Note: the coefficients (the numbers you multiply by, such as “5” in 5x) can be different.

Consider terms as 8y, 9y, 5y, and -2y

Here all four terms are like terms because y is the common variable.

Consider another example; \( \scriptsize 3xy^2,\: \normalsize \frac{1}{2} \scriptsize xy^2,\: 7xy^2 \: and \: \normalsize \frac{3}{4} \scriptsize xy^2 \)

Here also all four terms are like terms because xy²  is the common variable.

In the above example, 5xy is not a like term because xy is not raised to the power of 2.

Example 2.2.1:

Simplify:

(a) \( \scriptsize 4a \: + \: 3b \: + \: 2a \: + \: b \)
(b) \( \scriptsize 8x \: + \: 5y \: – \: 5x \: – \: 3y\: + \: 1 \)

Solution