Cambridge International Mathematics

140 Exponents and surds (Chapter 6)

Example 22 Self Tutor

Expand and simplify:

a

p

2(

p

2+

p

3) b

p

3(6¡ 2

p

3)

a

p

2(

p

2+

p

3)

=

p

2 £

p

2+

p

2 £

p

3

=2+

p

6

b

p

3(6¡ 2

p

3)

=(

p

3)(6 +¡ 2

p

3)

=(

p

3)(6) +(

p

3)(¡ 2

p

3)

=6

p

3+¡ 6

=6

p

3 ¡ 6

Example 23 Self Tutor

Expand and simplify:

a ¡

p

2(

p

2+3) b ¡

p

3(7¡ 2

p

3)

a ¡

p

2(

p

2+3)

=¡

p

2 £

p

2+¡

p

2 £ 3

=¡ 2 ¡ 3

p

2

b ¡

p

3(7¡ 2

p

3)

=(¡

p

3)(7¡ 2

p

3)

=(¡

p

3)(7) +(¡

p

3)(¡ 2

p

3)

=¡ 7

p

3+6

Example 24 Self Tutor

Expand and simplify: (3¡

p

2)(4 + 2

p

2)

(3¡

p

2)(4 + 2

p

2)

=(3¡

p

2)(4) +(3¡

p

2)(2

p

2)

=12¡ 4

p

2+6

p

2 ¡ 4

=8+2

p

2

Example 25 Self Tutor

Expand and simplify:

a (

p

3+2)^2 b (

p

3 ¡

p

7)^2

a (

p

3+2)^2

=(

p

3)^2 +2£

p

3 £2+2^2

=3+4

p

3+4

=7+4

p

3

b (

p

3 ¡

p

7)^2

=(

p

3)^2 ¡ 2 £

p

3 £

p

7+(

p

7)^2

=3¡ 2

p

21 + 7

=10¡ 2

p

21

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Y:\HAESE\IGCSE01\IG01_06\140IGCSE01_06.CDR Monday, 15 September 2008 3:21:04 PM PETER