How do you combine like terms in algebra?

One major objective of working with algebraic expressions is to write them as simply as possible and in a logical, generally accepted arrangement. When there is more than one term (one or more factors multiplied together and separated from other terms by + or -), then you need to check to see whether they can be combined with other terms that are "like" them.

Numbers, by themselves without letters or variables, are "like" terms. You can combine 14 and 8 because you know what they are and know the rules. For instance, 14 + 8 = 22, 14 - 8 = 6, 14(8) = 112, and so on. Most numbers can be written so that they can combine with one another. Fractions can be added if they have a common denominator. Decimals can be subtracted if you line up the decimal points.

The exception to this is that some numbers, written under a radical, can't be combined. These numbers are called "irrational." This is a good name for them, because they sometimes are difficult to manipulate.

Algebraic expressions involving variables or letters have to be dealt with carefully. Because the numbers that the letters represent aren't usually known, you can't add or subtract terms with different letters. The expression 2a + 3b has to stay that way. That's as simple as you can write it. But, the expression 4c + 3c can be simplified. You don't know what c represents, but you can combine the terms to tell how many of them you have (even though you don't know what they are!): 4c + 3c = 7c.