42 Algebra (Expansion and factorisation) (Chapter 1)Activity Algebraic common factor maze
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To find your way through this maze, follow the given instructions. After you have completed the maze
you may like to construct your own maze for a friend to follow.Instructions:1 You are permitted to move
horizontally or vertically butnot
diagonally.
2 Start at the starting term, 12 .A
move to the next cell is only
possible if that cell has a factor
in common with the one you are
presently on.
3 Try to get to the exit following the
rules above.Factorisationis the process of writing an expression as aproductof itsfactors.
Factorisationis the reverse process of expansion.Inexpansionswe have toremove brackets, whereas infactorisationwe have toinsert brackets.Notice that 3(x+2) is theproduct of two factors, 3 andx+2.
The brackets are essential, since,
in 3(x+2)the whole of x+2is multiplied by 3
whereas in 3 x+2only thexis multiplied by 3.expansion3(x+2)=3x+6factorisation
To factorise an algebraic expression involving a number of terms we look for the HCF of the terms and
write it in front of a set of brackets. We then find the contents of the brackets.
For example, 5 x^2 and 10 xy have HCF 5 x.So, 5 x^2 +10xy= 5 x£x+ 5 x£ 2 y
=5x(x+2y)FACTORISE FULLY
Notice that 4 a+ 12 = 2(2a+6) is not fully factorised as (2a+6) still has a common factor of 2
which could be removed. Although 2 is a common factor it is not thehighestcommon factor. The HCF is
4 and so
4 a+12=4(a+3) is fully factorised.G FACTORISING WITH COMMON FACTORS [2.8]
6 m 2 a 3 9 c^23 c c^282 p^2
4 m mn 6 n 5 c 25 5 m 12 4 p
8 y xy 2 6 a 5 a mn 6 n^27
7 y 21 3 z 5 x 3 y y^23 p p exit
ab 7 a yz xy 15 x xy p^27
17 pq 3 q q^2637 b b^26
start 12 5 10 10 b 12 y^29 b 3 b
6 a a^25 a 3 a 4 x xy 2 x x^2IGCSE01
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_01\042IGCSE01_01.CDR Thursday, 11 September 2008 9:08:23 AM PETER