Cambridge Additional Mathematics

(singke) #1
Surds, indices, and exponentials (Chapter 4) 115

3 Factorise:
a 4 x+ 9(2x)+18 b 4 x¡ 2 x¡ 20 c 9 x+ 9(3x)+14
d 9 x+ 4(3x)¡ 5 e 25 x+5x¡ 2 f 49 x¡ 7 x+1+12

Example 20 Self Tutor


Simplify:

a
6 n
3 n

b
4 n
6 n

a
6 n
3 n
or
6 n
3 n

=
2 n 3 n
3 n
=

¡ 6
3

¢n

=2n =2n

b
4 n
6 n
or
4 n
6 n

=
2 n 2 n
2 n 3 n
=

¡ 4
6

¢n

=
2 n
3 n
=

¡ 2
3

¢n

4 Simplify:

a
12 n
6 n

b
20 a
2 a

c
6 b
2 b

d
4 n
20 n

e
35 x
7 x
f
6 a
8 a
g
5 n+1
5 n
h
5 n+1
5

Example 21 Self Tutor


Simplify:

a
3 n+6n
3 n

b
2 m+2¡ 2 m
2 m

c
2 m+3+2m
9

a
3 n+6n
3 n
=
3 n+2n 3 n
3 n

=
3 n(1 + 2n)
3 n
=1+2n

b
2 m+2¡ 2 m
2 m

=
2 m 22 ¡ 2 m
2 m

=
2 m(4¡1)
2 m
=3

c
2 m+3+2m
9

=
2 m 23 +2m
9

=
2 m(8 + 1)
9
=2m

5 Simplify:

a
6 m+2m
2 m
b
2 n+12n
2 n
c
8 n+4n
2 n

d
12 x¡ 3 x
3 x
e
6 n+12n
1+2n
f
5 n+1¡ 5 n
4

g
5 n+1¡ 5 n
5 n

h
4 n¡ 2 n
2 n

i
2 n¡ 2 n¡^1
2 n
6 Simplify:
a 2 n(n+1)+2n(n¡1) b 3 n

³n¡ 1
6

́
¡ 3 n

³n+1
6

́

1

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Y:\HAESE\CAM4037\CamAdd_04\115CamAdd_04.cdr Tuesday, 14 January 2014 2:28:32 PM BRIAN

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