Like Terms
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Remember that variables represent a particular value in the real world. It could be the number of hours you work each week, the number of tickets you need to sell, or how much carpet you need for each room in the house. You wouldn't add the number of tickets you sell to the number of square feet of carpet needed. That just doesn't make sense. You would add the number of hours you worked in a month: 35h + 40h+ 20h + 30h = 125h. But you wouldn't add the number of tickets sold to the number of square feet of carpet. 5t + 35c cannot be added together as they are not like terms. Review this brief definition and examples in this encyclopedia entry.
Terms are like terms if they have the same variables with the same exponents.
Examples of like terms
| Term 1 | Term 2 |
|---|---|
| $$3x^2$$ | $$14x^2$$ |
| $$24$$ | $$77$$ |
| $$2a^2b^3$$ | $$12a^2b^3$$ |
Examples of unlike terms
| Term 1 | Term 2 | Reason |
|---|---|---|
| $$3x^2$$ | $$14x$$ | Different exponents |
| $$24$$ | $$77a$$ | Different variables |
| $$2a^2b^3$$ | $$2a^2b^2$$ | Different exponents on b |
Source: All Math Words Encyclopedia, https://www.allmathwords.org/en/l/liketerms.html
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