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Combining Like Terms
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Combining Like Terms
Help plan a pop-up game booth by simplifying algebraic expressions. Combine only terms with the same variable part and exponent. Show your steps for multi-step problems.
Spot the Like Terms
Look for terms with identical variable parts and exponents.
1.At the booth, prize tickets are tracked with variables. Which pair can be combined: 6p and 2p, or 6p and 2q? Choose the pair and explain what makes them alike.
2.Select all terms that are like terms with 4xy: 7xy, −3x, 2yx, 5x²y.
- 7xy
- −3x
- 2yx
- 5x²y
3.A game score is recorded as 5x² + 3x − 2x² + 4 − 7x. Group the like terms by writing each group together.
Simplify the Booth’s Expressions
Combine like terms. Keep unlike variable parts separate.
4.A sign lists the ticket total as 8t + 5t. Simplify the expression.
5.The booth has 9 blue tokens, then gives away 4 blue tokens and receives 6 bonus tokens. The expression is 9b − 4b + 6. Simplify it.
6.Two game stations record points as 7a + 3c − 2a + 5c. Combine like terms and show your grouping.
7.A prize counter’s expression is 6m − 4n + 3m + 7n − 2m. Simplify it.
Distribute, Then Combine
Use the distributive property before collecting like terms.
8.The cost of three identical game bundles is written 3(2x + 4) + x. Expand and simplify.
9.Simplify the booth total: 2(3y − 5) + 4y − 1. Show how you distribute and combine.
10.A helper simplifies 5(2p + 1) − 3p as 10p + 1 − 3p = 7p + 1. Identify the mistake and write the correct simplification.
11.In your own words, explain what makes two terms like terms. Include one example of terms that can be combined and one pair that cannot.
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