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Collecting Like Terms Worksheet

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Collecting Like Terms Worksheet

A market stall packs fruit into boxes. The letters stand for different kinds of box: a is an apple box, b is a banana box and c is a cherry box. Like terms have the same letter part, so 4a and 3a can be combined, but a and b cannot. Collect the coefficients of matching letters and keep unlike terms separate. Simplify each expression fully.

Warm-up: spot and combine

Remember: the number in front of a letter is its coefficient. If there is no number, the coefficient is 1. For example, 5a + 2a = 7a.

1.Simplify the apple-box expression 6a + 3a.
2.Simplify 8b − 5b. Which expression is correct?
  • 3b
  • 13b
  • 3
  • −3b
3.A customer orders 4a + 2b + 3a apple and banana boxes. Collect the like terms and simplify the expression.
4.True or false: 5a and 5b are like terms because both have a coefficient of 5.
TrueFalse
5.Simplify the stall's expression for a mixed order: 7a + 4b − 2a + b.

Take it further

Watch the signs as carefully as the coefficients. A term with no written coefficient has coefficient 1; for example, −c means −1c.

6.Simplify 9c − 4c + c.
7.Simplify the expression 3a + 6b − a − 2b + 4c. Keep unlike terms separate.
8.Match each expression to its simplified form.
  • 4a + 2a
  • 7b − 3b
  • 2a + 3b + a
  • 3a + 3b
  • 4b
  • 6a
9.A till receipt shows 5a + 3b − 2a + 4b − a. Simplify it, showing how you group the apple-box and banana-box terms.
10.A customer writes 6a + 2b − 3a + 5b − 2a. Simplify the expression and explain why the a-terms can be combined but the b-terms cannot be combined with them.

2 printable pages

  • Fruit-box key and examples for collecting like terms in algebra.

    Page 1

  • Market-stall practice simplifying expressions by collecting like terms.

    Page 2

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