Everything Maths Grade 10

Common factors EMAH

Factorising based on common factors relies on there being factors common to all the terms.

For example, 2 x 6 x^2 can be factorised as follows:

2 x 6 x^2 = 2x(1 3 x)

And2(x1)a(x1)can be factorised as follows:

(x1)(2a)

VISIT:

The following video shows an example of factorising by taking out a common factor.

See video:2DHZatwww.everythingmaths.co.za

Worked example 10: Factorising using a switch around in brackets

QUESTION

Factorise:

5(a2)b(2a)

SOLUTION

Use a “switch around” strategy to find the common factor.

Notice that 2 a=(a2)

5(a2)b(2a) = 5(a2)[b(a2)]

= 5(a2) +b(a2)

= (a2)(5 +b)

Exercise 1 – 5:

Factorise:

1. 12 x+ 32y 2. 2 ab^2 4 a^2 b 3. 18 ab 3 bc


2. 12 kj+ 18kq 5. 12 a+ 24a^3 6. 2 ab 8 a


3. 24 kj 16 k^2 j 8. a^2 bb^2 a 9. 72 b^2 q 18 b^3 q^2


4. 125 x^6 5 y^2 11. 6 x^2 + 2x+ 10x^3 12. 2 xy^2 +xy^2 z+ 3xy


5. 12 k^2 j+ 24k^2 j^2 14. 3 a^2 + 6a 18 15. 7 a+ 4

For more exercises, visit http://www.everythingmaths.co.za and click on ’Practise Maths’.

1.2DJ2 2.2DJ3 3.2DJ4 4.2DJ5 5.2DJ6 6.2DJ7 7.2DJ8 8.2DJ9

9.2DJB 10.2DJC 11.2DJD 12.2DJF 13.2DJG 14.2DJH 15.2DJJ

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Chapter 1. Algebraic expressions 21