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Factorising Algebraic Expressions

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Factorising Algebraic Expressions

Factorising rewrites a sum or difference as a product. Find the greatest common factor (GCF) shared by every term, then divide each term by it. For example, 6x + 18 = 6(x + 3), because both terms are divisible by 6.

Recognising common factors

1.What is the greatest common factor of 15x and 25?

2.Which equation shows a correct factorisation?

12b + 18 = 6(2b + 3)
9c - 27 = 3(3c - 6)
14d + 7 = 7(2d)
8e - 20 = 4(2e - 20)

Factorising practice

Factorise each expression by taking out its greatest common factor. For the final question, factorise the expression and expand your result to check it.

3.Factorise 9x + 27.

4.Factorise 14y − 35.

5.Factorise 12a + 48.

6.Factorise 18m − 30.

7.Factorise 5p + 40.

8.Factorise 4q + 24, then expand your factorised expression to check your answer. Show your working.

Using factorising in context

9.A sports club has 20 netballs and 15 rugby balls. It wants to make the greatest possible number of identical equipment sets, using all the balls. What is the maximum number of sets, and how many of each ball will be in a set? Show how the common factor helps.

10.A bike hire shop charges $8 for each hour plus a one-off $24 booking fee. The total cost for h hours is 8h + 24 dollars. Factorise the expression and explain what each factor represents.

11.A rectangle has an area of 12w + 36 square metres and a width of 12 metres. Factorise the area expression, then find the rectangle's length.