MathsFreePrintable

Expanding Algebraic Expressions

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Expanding Algebraic Expressions

Expand each expression by multiplying every term in a bracket. Simplify by collecting like terms where possible. Show working for the longer expressions.

Distributive Property

1.Use the distributive property to calculate 4 × (7 + 2).

2.Use the distributive property to calculate 3 × (10 − 4).

3.Expand 5(m + 4).

4.Expand 6(p − 3).

Expanding Single Brackets

5.Expand and simplify 4(2x + 3).

6.Expand and simplify 3(5y − 2).

7.Expand and simplify 2a(3a + 7).

8.Which expression is the correct expansion of 5(2x − 3)?

10x − 3
10x − 15
7x − 15
10x + 15

Double Brackets and Area

9.Use the area model to expand (x + 2)(x + 5). Fill each cell with the product of its row and column labels, then collect the terms.

10.Expand and simplify (x + 6)(x + 2).

11.Expand and simplify (x + 7)(x − 3).

12.Expand and simplify (3x + 2)(x + 4).

Combining Expansions

13.Expand and simplify 2x(x + 3) − (x − 5).

14.Expand and simplify 3(x − 4) + 2(2x + 1).

15.Expand and simplify (x + 3)(x − 2) + 4(x + 1).

16.Select every statement that describes a possible error when expanding algebraic expressions.

Multiplying the term outside a bracket by only the first term inside
Forgetting to distribute a negative sign across all terms
Combining unlike terms, such as x and x²
Collecting like terms after expanding

17.Match each expression to its expanded form: 4(x + 3); (x + 2)(x + 5); 2x(x − 4); (3x + 1)(x + 2).

4(x + 3)
(x + 2)(x + 5)
2x(x − 4)
(3x + 1)(x + 2)

2x² − 8x
4x + 12
x² + 7x + 10
3x² + 7x + 2

18.A bookshop packs a rectangular display with length (2x + 4) metres and width (x + 3) metres. Write an expression for its area, then expand and simplify it.

19.In one or two sentences, explain how the distributive property helps you expand a bracket such as 3(x + 4).

20.State one reliable method for expanding two brackets, then demonstrate it on (x + 1)(x + 4).