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New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
1
© 2009 Chung Tai Educational Press. All rights reserved.
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.
=
=
=
=
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
2
© 2009 Chung Tai Educational Press. All rights reserved.
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.
∴
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
3
© 2009 Chung Tai Educational Press. All rights reserved.
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 .
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
4
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.4 (page 3.10) Expand the following.
(a)
) () ()3)(3( 22
=
−=−+ xx
(b)
)54)(54(
=
=+− xx
(c)
)52)(52(
=
=−+ yxyx
Classwork 3.5 (page 3.10) Expand the following.
(a)
) () ()73)(73( 22
=
−=+−−− rr
(b)
) )( ()23)(32(
=
=
=++− stts
(c)
)52)(25(3
=
=
=
=+− pqqp
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
5
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.6 (page 3.11) Expand the following.
(a)
))((
=
=−+ bccbcc
(b)
))(( 22
=
=
=−+ vvvv
Classwork 3.7 (page 3.13) Expand the following.
(a)
) () )( (2) ()34( 222
=
++=+x
(b)
)23( 2
=
=+ x
(c)
)52( 2
=
=+ yx
(d)
)73( 2
=
=
=+− yx
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
6
© 2009 Chung Tai Educational Press. All rights reserved.
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
Classwork 3.9 (page 3.15) Expand the following.
(a)
) () )( (2) ()13( 222
=
+−=−x
(b)
)52( 2
=
=− x
(c)
)29( 2
=
=− yx
(d)
)]34(2[ 2
=
=
=
=−− yx
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
7
© 2009 Chung Tai Educational Press. All rights reserved.
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
=
=
=
=
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
8
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.12 (page 3.20) Factorize the following.
(a)
) )( (
) )( (28
=
=+ yzxy
(b)
84
=
=− efce
(c)
412
=
=
=−− qrpq
Classwork 3.13 (page 3.20) Factorize the following.
(a)
2025 32
=
=
=− xyyx
(b)
128 22
=
=
=
=+− pqqp
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
9
© 2009 Chung Tai Educational Press. All rights reserved.
(c)
156 2
=
=
=
=−− srrs
Classwork 3.14 (page 3.21) Factorize the following.
(a)
123224 23
=
=+− xxx
(b)
27612 235
=
=+− yyy
(c)
20155 632
=
=
=+−− zzz
Classwork 3.15 (page 3.21) Factorize the following.
(a) ) )( ()3(5)3( =+−+ bababa
(b)
)21()12(
=
=
=−−− ccdc
(c)
)5()5(3
=
=+−+ effee
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
10
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.16 (page 3.21) Factorize the following.
(a)
)(5)( 2
=
=
=−+− yxyx
(b)
)(6)(8 2
=
=
=
=+−+ vwwv
(c)
)2(2)2(6 2
=
=
=
=
=−−−− tuut
Classwork 3.17 (page 3.24) Factorize the following.
(a)
=
=+++ bcacbxax
(b)
=
=−−+ cycxbybx
Classwork 3.18 (page 3.24) Factorize the following.
(a)
3223
=
=
=−−+ acbcba
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
11
© 2009 Chung Tai Educational Press. All rights reserved.
(b)
76212
=
=
=+−− bxaybyax
Classwork 3.19 (page 3.25) Factorize the following.
(a)
2525 23
=
=−+− ttt
(b)
355284 23
=
=−−+ xxx
Classwork 3.20 (page 3.25) Factorize the following.
(a)
222
=
=
=−+−+− bambmam
(b)
26432
=
=
=−+−+− ybxayxbyax
Classwork 3.21 (page 3.27) Factorize the following.
(a)
6 65 22
=
=
+++=++ xxx
(b)
483 2
=
=
=+− xx
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
12
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.22 (page 3.29) Factorize the following.
(a)
4 2
=
=− x
(b)
81 2
=
=
=+− x
(c)
149 2
=
=−x
(d)
1625 22
=
=− yx
Classwork 3.23 (page 3.29) Factorize the following.
(a)
82 2
=
=
=−x
(b)
483 22
=
=
=− yx
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
13
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.24 (page 3.29) Factorize the following.
(a)
)( 22
=
=−+ ayx
(b)
)( 22
=
=
=+− yxx
Classwork 3.25 (page 3.30) Factorize the following.
(a)
)3()2( 22
=
=
=−−+ yxyx
(b)
)45()54( 22
=
=
=
=−−− yxyx
Classwork 3.26 (page 3.30) Factorize the following.
(a)
2222
=
=+−− bcacba
(b)
42 22
=
=
=
=−−− ddecec
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
14
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.27 (page 3.30) Without using a calculator, find the values of the following.
(a)
3367 22
=
=
=−
(b)
245255 22
=
=
=−
Classwork 3.28 (page 3.33) Factorize the following.
(a)
121222
=
=++ xx
(b)
25309 22
=
=++ yxyx
Classwork 3.29 (page 3.33) Factorize the following.
(a)
1682
=
=+− xx
(b)
9124 22
=
=+− yxyx
New Trend Mathematics (2nd Edition) S2A - Worksheet for Classwork - Chapter 3
15
© 2009 Chung Tai Educational Press. All rights reserved.
Classwork 3.30 (page 3.34) Factorize the following.
(a)
882 2
=
=
=+− xx
(b)
21218 22
=
=
=++ yxyx
Classwork 3.31 (page 3.34) Factorize the following.
(a)
1)(2)( 2
=
=++−+ baba
(b)
8)(8)(2 2
=
=
=
=+−+− yxyx
Classwork 3.32 (page 3.34) Factorize the following.
(a)
2 222
=
=
=
=−+− zyxyx
(b)
444 222
=
=
=
=++− yxyzx