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