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Algebraic Expressions Worksheet
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Algebraic Expressions Worksheet
Simplify, expand and factorise each expression. Show your working where space is provided. Use metres and square metres where stated.
Simplifying and Expanding
1.Simplify 9x − 4x + 2x.
2.Simplify 6a − 3b + 2a + 8b.
3.Simplify 4x² + 3x − x² + 6x.
4.Expand and simplify 4(x − 3).
5.Expand and simplify −3(2y + 5).
6.Expand and simplify x(3x − 4).
7.Use an area model to expand (x + 4)(x + 3). Label the partial products and write the simplified result.
Draw and label your area model here.
8.Which property is illustrated by 7x + 2x = 2x + 7x?
- Commutative property
- Associative property
- Distributive property
- Identity property
9.Which property is illustrated by 3(x + 6) = 3x + 18?
- Commutative property
- Associative property
- Distributive property
- Identity property
10.Which property is illustrated by (4x + 2x) + 5x = 4x + (2x + 5x)?
- Commutative property
- Associative property
- Distributive property
- Identity property
Factorising
11.Factorise 10x + 15 by taking out the highest common factor.
12.Factorise 6x² − 9x by taking out the highest common factor.
13.Factorise 21y + 14 by taking out the highest common factor.
14.Factorise the quadratic expression x² + 8x + 15.
15.Factorise the quadratic expression x² − 9x + 20.
16.Factorise x² + 9x + 18. Show how you select the two numbers needed.
Algebra in Context
17.A rectangular vegetable plot has length (x + 6) metres and width (x + 1) metres. Write an expression for its area in factored form.
18.Expand the area expression for a rectangular plot with length (x + 6) metres and width (x + 1) metres.
19.A rectangular plot measures (x + 6) metres by (x + 1) metres. Find its area when x = 4.
20.Describe why multiplying a number across a bracket gives an equivalent expression. Include an algebraic example.
21.Factorise 3x² + 11x + 6 completely.
4 printable pages
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