Cambridge Additional Mathematics

114 Surds, indices, and exponentials (Chapter 4)

2 Expand and simplify:

a (2x¡1)(2x+3) b (3x+ 2)(3x+5) c (5x¡2)(5x¡4)

d (2x+3)^2 e (3x¡1)^2 f (4x+7)^2

3 Expand and simplify:

a (x

1

(^2) + 2)(x
1
(^2) ¡2) b (2x+ 3)(2x¡3) c (x
1
(^2) +x¡
1
(^2) )(x
1
(^2) ¡x¡
1
(^2) )
d (x+
2
x
)^2 e (7x¡ 7 ¡x)^2 f (5¡ 2 ¡x)^2
g (x
2
(^3) +x
1
(^3) )^2 h (x
3
(^2) ¡x
1
(^2) )^2 i (2x
1
(^2) ¡x¡
1
(^2) )^2

FACTORISATION AND SIMPLIFICATION

Example 18 Self Tutor

Factorise: a 2 n+3+2n b 2 n+3+8 c 23 n+2^2 n

a 2 n+3+2n

=2n 23 +2n

=2n(2^3 +1)

=2n£ 9

b 2 n+3+8

=2n 23 +8

= 8(2n)+8

= 8(2n+1)

c 23 n+2^2 n

=2^2 n 2 n+2^2 n

=2^2 n(2n+1)

Example 19 Self Tutor

Factorise: a 4 x¡ 9 b 9 x+ 4(3x)+4

a 4 x¡ 9

=(2x)^2 ¡ 32 fcompare a^2 ¡b^2 =(a+b)(a¡b)g

=(2x+ 3)(2x¡3)

b 9 x+ 4(3x)+4

=(3x)^2 + 4(3x)+4 fcompare a^2 +4a+4g

=(3x+2)^2 fas a^2 +4a+4=(a+2)^2 g

EXERCISE 4E.2

1 Factorise:

a 52 x+5x b 3 n+2+3n c 7 n+7^3 n

d 5 n+1¡ 5 e 6 n+2¡ 6 f 4 n+2¡ 16

2 Factorise:

a 9 x¡ 4 b 4 x¡ 25 c 16 ¡ 9 x

d 25 ¡ 4 x e 9 x¡ 4 x f 4 x+ 6(2x)+9

g 9 x+ 10(3x)+25 h 4 x¡14(2x)+49 i 25 x¡4(5x)+4

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\114CamAdd_04.cdr Tuesday, 14 January 2014 2:28:29 PM BRIAN