Classwork 3.1 (page 3.5) -...

New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3

1

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Classwork 3.1 (page 3.5) Prove that the following equations are identities.

(a) 18)3(24)12(2 −+−=−− xxx

Proof: L.H.S.

4)12(2

=

=

−−= xx

R.H.S.

18)3(2

=

=

−+−= x

L.H.S. ≡ R.H.S.

∴

(b) 8)2()4)(2( −−=−+ xxxx

Proof:

L.H.S.

=

=

=

=


2


R.H.S.

=

=

L.H.S. ≡ R.H.S.

∴

Classwork 3.2 (page 3.5) Prove that the following equations are NOT identities.

(a) 3)1(2)1(5)2(3 −+=−−+ xxx

Proof: L.H.S.

)1(5)2(3

=

=

−−+= xx

R.H.S.

3)1(2

=

=

−+= x

L.H.S. ≡/ R.H.S.

∴

(b) 8)4(7)45(2)3(4 −+=−+− xxx

Proof: L.H.S.

=

=

=

R.H.S.

=

=

=

L.H.S. ≡/ R.H.S.

∴


3


Classwork 3.3 (page 3.6) (a) If QPxxxx ++≡−+ 2)5)(2( , find the constants P and Q.

Solution:

L.H.S.

=

=

=

=

QPxx ++≡ 2

∴ By comparing the like terms on the L.H.S. and R.H.S., we have

=P and =Q .

(b) If CBxAxxx ++≡−+ 2)52)(13( , find the constants A, B and C.

Solution:

L.H.S.

=

=

=

=

CBxAx ++≡ 2

∴ By comparing the like terms on the L.H.S. and R.H.S., we have

=A , =B and =C .


4


Classwork 3.4 (page 3.10) Expand the following.

(a)

) () ()3)(3( 22

=

−=−+ xx

(b)

)54)(54(

=

=+− xx

(c)

)52)(52(

=

=−+ yxyx


(a)

) () ()73)(73( 22

=

−=+−−− rr

(b)

) )( ()23)(32(

=

=

=++− stts

(c)

)52)(25(3

=

=

=

=+− pqqp


5



(a)

))((

=

=−+ bccbcc

(b)

))(( 22

=

=

=−+ vvvv


(a)

) () )( (2) ()34( 222

=

++=+x

(b)

)23( 2

=

=+ x

(c)

)52( 2

=

=+ yx

(d)

)73( 2

=

=

=+− yx


6


Classwork 3.8 (page 3.13) (a) Expand

2)1( y+ .

Solution:

)1( 2

=

=+ y

(b) By using the result of (a), expand 2)1( qp ++ .

Solution: Let =y .

)1( 2

=

=

=

=++ qp


(a)

) () )( (2) ()13( 222

=

+−=−x

(b)

)52( 2

=

=− x

(c)

)29( 2

=

=− yx

(d)

)]34(2[ 2

=

=

=

=−− yx


7


Classwork 3.10 (page 3.16) (a) Expand

2)3( −r .

Solution:

)3( 2

=

=−r

(b) By using the result of (a), expand 2)3( −+ dc .

Solution:

Let =r .

)3( 2

=

=

=

=−+ dc

Classwork 3.11 (page 3.16) Without using a calculator, find the value of each of the following.

(a)

) () )( (2) (

) (202

22

22

=

=

++=

+=

(b)

3902

=

=

=

=


8


Classwork 3.12 (page 3.20) Factorize the following.

(a)

) )( (

) )( (28

=

=+ yzxy

(b)

84

=

=− efce

(c)

412

=

=

=−− qrpq


(a)

2025 32

=

=

=− xyyx

(b)

128 22

=

=

=

=+− pqqp


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(c)

156 2

=

=

=

=−− srrs


(a)

123224 23

=

=+− xxx

(b)

27612 235

=

=+− yyy

(c)

20155 632

=

=

=+−− zzz


(a) ) )( ()3(5)3( =+−+ bababa

(b)

)21()12(

=

=

=−−− ccdc

(c)

)5()5(3

=

=+−+ effee


10



(a)

)(5)( 2

=

=

=−+− yxyx

(b)

)(6)(8 2

=

=

=

=+−+ vwwv

(c)

)2(2)2(6 2

=

=

=

=

=−−−− tuut


(a)

=

=+++ bcacbxax

(b)

=

=−−+ cycxbybx


(a)

3223

=

=

=−−+ acbcba


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(b)

76212

=

=

=+−− bxaybyax


(a)

2525 23

=

=−+− ttt

(b)

355284 23

=

=−−+ xxx


(a)

222

=

=

=−+−+− bambmam

(b)

26432

=

=

=−+−+− ybxayxbyax


(a)

6 65 22

=

=

+++=++ xxx

(b)

483 2

=

=

=+− xx


12



(a)

4 2

=

=− x

(b)

81 2

=

=

=+− x

(c)

149 2

=

=−x

(d)

1625 22

=

=− yx


(a)

82 2

=

=

=−x

(b)

483 22

=

=

=− yx


13



(a)

)( 22

=

=−+ ayx

(b)

)( 22

=

=

=+− yxx


(a)

)3()2( 22

=

=

=−−+ yxyx

(b)

)45()54( 22

=

=

=

=−−− yxyx


(a)

2222

=

=+−− bcacba

(b)

42 22

=

=

=

=−−− ddecec


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Classwork 3.27 (page 3.30) Without using a calculator, find the values of the following.

(a)

3367 22

=

=

=−

(b)

245255 22

=

=

=−


(a)

121222

=

=++ xx

(b)

25309 22

=

=++ yxyx


(a)

1682

=

=+− xx

(b)

9124 22

=

=+− yxyx


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(a)

882 2

=

=

=+− xx

(b)

21218 22

=

=

=++ yxyx


(a)

1)(2)( 2

=

=++−+ baba

(b)

8)(8)(2 2

=

=

=

=+−+− yxyx


(a)

2 222

=

=

=

=−+− zyxyx

(b)

444 222

=

=

=

=++− yxyzx

Classwork 3.1 (page 3.5) -...

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