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Combining Like Terms
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Combining Like Terms
At a makers’ market, stallholders use letters to track bundles of items. Simplify each expression by combining terms with the same variable part. Remember: add or subtract the coefficients; keep the variable part unchanged.
Spot the like terms
Like terms have exactly the same variable part, including the same powers. Constants are like terms too.
1.Which pair contains like terms? Select one answer.
- 5a and 5a²
- −3mn and 8nm
- 4p and 4q
- 2x² and 2x
2.For each expression, group the like terms and simplify: (a) 6x + 2 + 3x − 5; (b) 4y + 2y² − y + 7y².
3.A stallholder records 7b + (−10b). Simplify the expression.
4.Match each expression on the left to its simplified form on the right.
- 3x + 5x − 2
- 6a − 2a + 9
- 4m² + m − m²
- 3m² + m
- 8x − 2
- 4a + 9
3r
−2s²
5
−7r
4s²
−3
5.From the expression sorting board, group terms with matching variable parts, then simplify 3r − 2s² + 5 − 7r + 4s² − 3.
6.True or false: 2xy + 6yx can be combined to make 8xy. Explain your decision.
7.A student simplifies 5x + 3x² − 2x as 6x². Identify the mistake and write the correct simplified expression.
8.Create an expression with exactly three terms that simplifies to 4a + 6. Use at least one negative coefficient and show your simplification.
9.Explain why 2p + 3q cannot be simplified to 5pq. Use the terms coefficient and variable part in your explanation.
10.Three craft orders are written as 2c + 4, 5c − 1 and −3c + 6. Write one expression for the total, then simplify it.
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