Three movie tickets and two movie tickets can be combined as five movie tickets. Three tickets and two popcorns cannot be renamed as five tickets because they are different items.
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Algebra 1 · Unit 1 · Micro-Lesson 4
Identify Like Terms
I candecide whether terms are like terms by comparing their variables and exponents.
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Why should I care?
Connect the Math to Real Life
Like terms represent the same kind of quantity. Recognizing them prevents us from combining amounts that do not belong together.
Important words
Build the Vocabulary
Read the meaning, then connect it to the example.
Like terms
Terms with exactly the same variables raised to exactly the same exponents.
Variable part
Every variable and exponent in a term, without its coefficient.
Unlike terms
Terms whose variables or exponents do not match exactly.
See the pattern
Worked Examples
3x² and −8x²
Both variable parts are x². The coefficients may be different.
x and x²
x means x¹, or one factor of x. x² means x · x, or two factors of x. Their exponents differ, so they cannot be combined.
4x and 4y
The coefficients match, but the variables do not. They describe different quantities.
A common question
Why Can’t We Combine x + x2?
Like terms must have the same variable raised to the same exponent. The invisible exponent on x is 1.
x = x1one factor of x≠x2 = x · xtwo factors of x
Think of them as different items: one T-shirt plus one pair of shoes cannot be renamed as two T-shirts. In the same way, x and x2 describe different quantities.
Try it yourself
8-Question Practice
Choose an answer, check your thinking, and use the hint if you need another try.