Algebra (Expansion

and factorisation)

1

Contents:

A The distributive law [2.7]

B The product(a+b)(c+d) [2.7]

C Difference of two squares [2.7]

D Perfect squares expansion [2.7]

E Further expansion [2.7]

F Algebraic common factors

G Factorising with common factors [2.8]

H Difference of two squares factorisation [2.8]

I Perfect squares factorisation [2.8]

J Expressions with four terms [2.8]

K Factorising x^2 +bx+c [2.8]

L Splitting the middle term [2.8]

M Miscellaneous factorisation [2.8]

Opening problem

#endboxedheading

A square garden plot is surrounded by a path

50 cm wide. Each side of the path isxm long,

as shown.

a Write an expression for the side length of

the garden plot.

b Use the difference of two squares

factorisation to show that the area of the

path is (2x¡1)square metres.

The study ofalgebrais vital for many areas of mathematics. We need it to manipulate equations, solve

problems for unknown variables, and also to develop higher level mathematical theories.

In this chapter we consider theexpansionof expressions which involve brackets, and the reverse process

which is calledfactorisation.

xm

0.5 m

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Y:\HAESE\IGCSE01\IG01_01\031IGCSE01_01.CDR Thursday, 11 September 2008 3:14:07 PM PETER