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Simplifying Algebraic Expressions
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Simplifying Algebraic Expressions
Simplify each expression by expanding brackets where needed and collecting like terms. Show your working when there is room.
Combine Like Terms
1.Simplify: 4x + 7x.
2.Simplify: 9y − 3y + 2y.
3.Simplify: 5a + 8 + 3a − 2.
4.Simplify: 6m + 4n − 2m + 7n.
5.Select every expression that is already simplified.
- 3r + 5s − 2
- 7b + 2b
- 4p − q + 6
- 2k + 3k + 1
Expand Brackets
6.Expand: 3(x + 5).
7.Expand: 5(y − 3).
8.Expand: 4(2a + 3).
9.Expand: 2(3m − 4n).
10.Which property allows the factor outside the brackets to be multiplied by each term inside them?
- Commutative property
- Distributive property
- Associative property
- Identity property
Expand and Simplify
11.Expand and simplify: 3(x + 2) + 4x.
12.Expand and simplify: 2(y − 4) + 5y + 1.
13.Expand and simplify: 5(2a + 1) − 6a.
14.Expand and simplify: 3(2m + 1) + 2(m − 5).
15.Match each expression to its simplified form.
- 2(x + 4) + 3x
- 4(y − 2) + y
- 3(a + 2)
- 6(b − 1) + 6
- D. 6b
- A. 3a + 6
- B. 5x + 8
- C. 5y − 8
Use Algebra in Context
16.At a fire station, Hana packs x hoses into each of 4 equipment lockers, then places 3 spare hoses nearby. Write and simplify an expression for the total number of hoses.
17.A rectangular training area has length (3y + 2) metres and width 5 metres. Using P = 2(length + width), write the simplified expression for its perimeter.
18.Decide whether each statement is true or false: 6x + 2x = 8x²; 3(a + 4) = 3a + 12; 5p + 2q cannot be simplified further; 4(x − 2) + x = 5x − 8.
TrueFalse
19.In one or two sentences, explain what makes two algebraic terms like terms.
Challenge
20.Simplify: 2(3x − 4) + 5(x + 1) + 2x.
21.Simplify: 5(y + 2) − 3(y − 4) + 2y.
22.Write an expression containing brackets and like terms that simplifies to 7x + 9. Give one valid example.
23.State one part of simplifying algebraic expressions that you would like to practise more. There is no single correct response.
4 printable pages
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