Cambridge Additional Mathematics

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

(^111)
4037 Cambridge
cyan magenta yellow black Additional Mathematics
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_04\115CamAdd_04.cdr Tuesday, 14 January 2014 2:28:32 PM BRIAN