40 Algebra (Expansion and factorisation) (Chapter 1)b (x+ 1)(x¡3)(x+2)
=(x^2 ¡ 3 x+x¡3)(x+2) fexpanding the first two factorsg
=(x^2 ¡ 2 x¡3)(x+2) fcollecting like termsg
=x^3 ¡ 2 x^2 ¡ 3 x+2x^2 ¡ 4 x¡ 6 fexpanding the remaining factorsg
=x^3 ¡ 7 x¡ 6 fcollecting like termsgEXERCISE 1E
1 Expand and simplify:
a (x+ 2)(x^2 +x+4) b (x+ 3)(x^2 +2x¡3)
c (x+ 3)(x^2 +2x+1) d (x+ 1)(2x^2 ¡x¡5)
e (2x+ 3)(x^2 +2x+1) f (2x¡5)(x^2 ¡ 2 x¡3)
g (x+ 5)(3x^2 ¡x+4) h (4x¡1)(2x^2 ¡ 3 x+1)
2 Expand and simplify:
a (x+1)^3 b (x+3)^3 c (x¡4)^3
d (x¡3)^3 e (3x+1)^3 f (2x¡3)^3
3 Expand and simplify:
a x(x+ 2)(x+4) b x(x¡3)(x+2) c x(x¡4)(x¡5)
d 2 x(x+ 2)(x+5) e 3 x(x¡2)(3¡x) f ¡x(2 +x)(6¡x)
g ¡ 3 x(3x¡1)(x+4) h x(1¡ 5 x)(2x+3) i (x¡2)(x+ 2)(x¡3)
4 Expand and simplify:
a (x+ 4)(x+ 3)(x+2) b (x¡3)(x¡2)(x+4) c (x¡3)(x¡2)(x¡5)
d (2x¡3)(x+ 3)(x¡1) e (3x+ 5)(x+ 1)(x+2) f (4x+ 1)(3x¡1)(x+1)
g (2¡x)(3x+ 1)(x¡7) h (x¡2)(4¡x)(3x+2)
5 State how many terms you would obtain by expanding the following:
a (a+b)(c+d) b (a+b+c)(d+e) c (a+b)(c+d+e)
d (a+b+c)(d+e+f) e (a+b+c+d)(e+f) f (a+b+c+d)(e+f+g)
g (a+b)(c+d)(e+f) h (a+b+c)(d+e)(f+g)Algebraic productsare products which contain variables.
For example, 6 c and 4 x^2 y are both algebraic products.
In the same way that whole numbers have factors, algebraic products are also made up of factors.For example, in the same way that we can write 60 as 2 £ 2 £ 3 £ 5 , we can write 2 xy^2 as 2 £x£y£y.
To find thehighest common factorof a group of numbers, we express the numbers as products of prime
factors. The common prime factors are then found and multiplied to give the highest common factor (HCF).
We can use the same technique to find the highest common factor of a group of algebraic products.F ALGEBRAIC COMMON FACTORS
Each term of the first
bracket is multiplied
by each term of the
second bracket.IGCSE01
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Y:\HAESE\IGCSE01\IG01_01\040IGCSE01_01.CDR Wednesday, 10 September 2008 2:07:16 PM PETER