Math 1 · Lesson 5 · part 4 of 5
What "like terms" means
A term (one of the pieces that are added) is one chunk of a line.
What "like terms" means
A term (one of the pieces that are added) is one chunk of a line. In 5x + 2x + (−9), the terms (the pieces that are added) are 5x, 2x and −9. Two terms are like terms (the terms with the same letter part) when their letter part matches exactly. The letter has to be the same. The exponent (the little raised number that says how many times the letter is multiplied by itself, from Lesson 3) has to match too. Like terms (the terms with the same letter part) combine with the distributive property run backwards (factoring, pulling out what the terms share, from Lesson 2). It looks like this: 5x + 2x = (5 + 2)x = 7x. Constants (plain numbers with no letter) are like terms (the terms with the same letter part) with each other. They have no letter to pull out, so you just add them: 6 + (−5) = 1. The associative property of addition (the terms change partners, the grouping moves) is what lets you group them first.
Here is a pair that cannot be combined: 4x + 7y. The letter parts are different, so there is nothing to pull out of both terms. Leave it as 4x + 7y, because that is already as short as it gets. If you cannot pull the same letter part out of both terms, they are not like terms (the terms with the same letter part).