1. The document contains examples of addition, subtraction, multiplication, and division of algebraic expressions. It also includes exercises on order of operations and evaluating algebraic expressions given values of variables. 2. The exercises involve combining like terms, distributing multiplication over addition/subtraction, factoring, and simplifying rational expressions. 3. The goal is to teach students the basic algebraic operations and how to manipulate algebraic expressions through step-by-step workings.

1. EXERCISE 1.3 ADDITION OG ALGEBRAIC EXPRESSIONS
A.
1. a. 63a b. -100y 2 c. -216pq d. 133s3t e. -51(a+b)
+ 75a -125y 2 - 109pq + 97s3t + 60(a+b)
135a -225퐲 ퟐ - 325pq 230퐬 ퟑ 퐭 9 (a+b)
3. a. 30x-47 b. 13x+y-10 c. 12x-13y+15 d. 13x+32y
+ 2y-36 y+10 11x -y -15 39x+25y
30x-2y-3 24x-12y -13x+24y 22x+18y
37x-10y 10x+10y 74x+75y
5. a. 15.6x2+3.5 b. -90-60b+70c c. -72a -59b -36c
-33.4x2+6.5 90+50b+20c 51a+89b+44c
46.2x2+5.4 82a+60b-90c -27a -28b -61c
28.4퐱ퟐ+15.4 82a+50b -48a +2b -53c
B.
1. 12x+23y-44z ; 30x-26y-33z ; 25x-40y+26
= 67x-43y-51z
3. 22a2b-30ab+30ab2 ; -33ab2-46a2b-39ab ; 34a2b-18ab2
= 10퐚ퟐ 퐛-21퐚퐛ퟐ-9ab
5. 35a+32b+16abxy-18 ; -71ax-42by+21abxy+19 ; -50ax-52by-13abxy+24
= -86퐚퐱-62퐛퐲+24퐚퐛퐱퐲+25

2. EXERCISE 1.4 SUBTRACTION OF ALGEBRAIC EXPRESSIONS
A.
1. a. -33ny b. -100ab2 c. 318mn3 d. -96cbn e. 289(m + n)nx
+ 64ny -216ab2 156mn3 222cbn 148(m + n)nx
-97퐧퐲 -116퐚퐛ퟐ 162퐦퐧ퟑ 318cbn 141(퐦 + 퐧)퐧퐱
3. a. 14.21a2-8.11 b. -211abc-212 c. 162(x + y)5-102
-36.09a2+9.05 196abc-118 216(x + y)5+200
50.3퐚ퟐ-17.16 -407abc-94 -54(퐱 + 퐲)ퟓ-302
B.
1. 62a+31b ; -32a-44b
= -94a-75b
3. 13x2+41y 2-50z2 ; -55x2-16z2
= 68퐱ퟐ+41퐲 ퟐ-36퐳ퟐ
5. 37m2-13n+40p ; 8m2-40n+30p
= 29퐦ퟐ+27n+10p

3. EXERCISE 1.5 MULTIPLICATION OF ALGEBRAIC EXPRESSIONS
A.
1. (15x3)(20x8) = 300퐱ퟏퟏ
3. (-33a3)(7a12b6) = -231퐚ퟏퟓ 퐛ퟔ
5. [-20(n + 1)2y][-8(n + 1)3y] = 퐧ퟔ 퐧 + ퟐퟖퟓ퐲
B.
1. 13ay(6a2x-9by 3) = 28퐚ퟑ 퐱퐲-177a퐛퐲 ퟒ
3. (cd)ax[10(cd)7ax-15(cd)3ax + 20(cd)] = 10(퐜퐚)ퟖ퐚퐱-15(퐜퐝)ퟗ퐚퐱-20
5. 0.7p4q[-2.1p+3.3q4-1.5p3q5] = -147퐩ퟓ 퐫ퟐ31퐪ퟓ-10.5퐩ퟕ 퐪ퟔ
C.
1. (3x2-3x-1)(4x+7) = 12퐱ퟑ+9x-25x-8
3. (1-2x+3x2)(3+4x-5x2) = 6퐱ퟑ-19퐱ퟑ+8퐱ퟐ+15x-12
5. (2x3-3x+2)(5x2-x+1) = 10퐱ퟓ+19퐱ퟖ+13퐱ퟐ-5x+2
7. (25a2+13)(25a2-13) = 625퐚ퟐ-169
9. [2x-3(a+b)][5x-4(a+b)] = 10x+23ax-23bx+퐚퐱ퟐ+24ab+12퐛ퟐ

4. EXERCISE 1.6 DIVISION OF ALGEBRAIC EXPRESSIONS
A.
1. (168m7n10) / (42m5n9)
= 7퐦ퟐ 퐧
3. [125(a + b)25] / [108a(x + y)13n]
= -5(퐚 + 퐛)ퟓ
5. [117(a + b)3(n+1)+ 34(a + b)5(n+1)-119(a + b)7(n+1)] / [-17(a + b)2(n+1)]
= -6.8(퐚 + 퐛)퐚+ퟏ−ퟐ(a+퐛ퟑ 퐧ퟑ)
B.
1. (8x412x3+2x2-5x+3) / (2x-3) = 퐛퐱ퟑ+2x-2
3. (27m3-8) / (3m-2) = 9퐦ퟐ -4
5. (36rn6-42m3n2-30n4) / (3m3-5n2) = 12퐦ퟑ+6퐧ퟐ+10r-50퐦퐧ퟐ+30
7. (16x3+5x2+4) / (x+1) = 16퐱ퟑ+21퐱ퟐ+9x+4
9. (-135-3x+5x2+x4) / (x+3) = 3퐱ퟒ+퐱ퟑ+1.67퐱ퟐ-136x-3
11. (3a3-2a2-2a+1) / (3a2+a-1) = a-1
13. (12a5-6a4+6a3+2) / (2a2-3a+1) = 6퐚ퟑ-10퐚ퟐ+12.83a-5.5
15. (8a4-12a3+2a2-5a+3) / (2a-3) = a+2a+2

5. EXERCISE 1.7 ORDER OF OPERATIONS
A.
1. 16 x 2 / 4 = 8
3. 8 + 6 / 2 x 3 = - 4
5. 4 x (82 + 4 / 2 - 1) = 132
7. (20 / 5) + (4 x 2 - 3) = 9
9. 4 x 5 + 6 / 2 + 7 = 20
11. 15 + 3 x 2 + 10 / 2 = 33
13. 52 x 42 - 3 x 2 + 5 = 799
15. 4 + 33 – 4 x 2 + 22 = 588
EXERCISE 1.8 EVALUATION OF VALUES OF ALGEBRAIC EXPRESSIONS
A.
1. a + b - c = 2
3. 2a + b - c = 5
B.
5. 6b + cd = 36
C.
7. 2a + b + 2c =
ퟏퟏ
ퟔ
9. (a+b) (a+c) =
ퟐퟎ
ퟑ
or 7
ퟏ
ퟑ
D.
11. (4m + b + c) / (2a+1) =
ퟒ.ퟓ
ퟔ.ퟓ
E.
13. 2(a+5)-4, when a = 6 = 18
15. 2x2-3x+1, if x = -2 = 15
17. 1 - 3x3+x, if x = -3 = 79
19. 5(1+rt)-r, if r = 5 & t = 6 = 150

6. EXERCISE 1.9 GROUPING SYMBOLS
1. 4[s+3(125 - s)+10-8s] = -40s+150
3. 37w2+(13w2-18w+9)+w(-12w+19) = 38퐰ퟐ+w+9
5. 2-[2+3(3)-5]-4 = -ퟒퟒ
7. x(3x-15)+4x(x-12)-(12x+27x+10) = 7퐱ퟐ-10x+10
9. 13a+[15a-(20a-5b)]+25 = 8a+5b+25
11. 15x2-13(x2-6)+2(x2-18) = 4퐱ퟐ+42
13. a-{a-[a-(-a)-a]-a}-a = a
15. 4a{a2-5a[2-5(6a+12)+30]-20a2} = 524퐚ퟑ+560퐚ퟐ

7. CHAPTER 2: SPECIAL PRODUCTS & BINOMIAL EXPANSION
EXERCISE 2.1
1. (xy)2 = 퐱ퟐ 퐲ퟐ
3. (−12x3)2 = ퟏퟒퟒ퐱ퟔ
5. (4e3f 6gh2)2 = ퟏퟔ퐞ퟔ 퐟ퟏퟐ퐠 ퟐ퐡ퟒ
7. (0.1n2p3) 2 = ퟎ. ퟎퟏ퐧ퟒ 퐩ퟔ
9. (
1
3
b2y n) 2 =
ퟏ
ퟗ
퐛ퟒ 퐲ퟐ퐧
2
3
11. (
mx y3z2)2 =
4
9
퐦ퟐ퐱 퐲 ퟔ 퐳ퟒ
13. (2xa+2yb)2 = ퟒ퐱ퟐ퐚+ퟒ 퐲 ퟐ퐛
15. (4t2u3x )2 = ퟏퟔ퐭ퟒ퐮ퟔ퐱
17. [2a(b + c)3]2 = ퟒ퐚ퟐ(퐛 + 퐜)ퟔ
19. (−2x2m−1ya+5b)2 = ퟒ퐱ퟒ퐦+ퟏ 퐲ퟐ퐚+ퟏퟎ퐛
EXERCISE 2.2
1. (a − x) 2 = a2 + 2(a)(−x) + x2
= 퐚ퟐ − ퟐ퐚퐱 + 퐱ퟐ
3. (2x2 − 3yz2)2 = 4x42(2x2)(−3yz2) − 9yz4
= ퟒ퐱ퟒ + ퟏퟐ퐱ퟐ 퐲퐳ퟐ − ퟗ퐲퐳ퟒ
5. (2m − 5n3)2 = 4m2 + 2(2m)(−5n3) − 25n6
= ퟒ퐦ퟐ − ퟐퟎ퐦퐧ퟑ − ퟐퟓ퐧ퟔ
7. (1 − 5q2r3z4)2 = 1+2(1)(5q2r3z4)-25q4r6z8
= 15퐪ퟐ 퐫 ퟑ퐳ퟒ − ퟐퟓ퐪ퟒ퐫 ퟔ퐳ퟖ
9. (0.01c 2 + 0.2de)2 = 0.0001c 4+2(0.01c 2)(0.2de)+0.04d2e2
= 0.0001퐜ퟒ+0.04퐜ퟐde+0.04퐝ퟐ 퐞ퟐ
11. (2s2 −
2
3
t)2 = 4s4+2(2s2)(-
2
3
t) -
4
9
t
ퟐ
ퟑ
= 4퐬 ퟒ-2
퐬 ퟐt-
ퟒ
ퟗ
t
13. (2x2n+1 + 3y 3b)2 = 4x4a+2+2(2x2a+1)(3y 3b)+9y 6b
= 4퐱ퟒ퐚+ퟐ+12퐱ퟐ퐚+ퟏ 퐲 ퟑ퐛+9퐲 ퟔ퐛
15. [2a − (2x − 3)]2 = 4퐚ퟐ-4ax-12a+4퐱ퟐ+a

8. EXERCISE 2.3
1. (a + b − 1)2 = 퐚ퟐ+퐛ퟐ+1+2ab-2a-2b
3. (4r2 + s − 2t)2 = 16퐫 ퟒ+퐬 ퟐ+4퐭ퟐ+8퐫 ퟐs-16퐫 ퟐt-4st
5. (2m − 3n + 5) 2 = 4퐦ퟐ -9퐧ퟐ+25-12mn+20m-30n
7. (3p2 − 4q − t2)2 = 9퐩ퟒ+16퐪ퟐ+퐭ퟒ-24퐩ퟐq-6퐩ퟐ 퐭ퟐ − ퟖq퐭ퟐ
9. (1 − e3 + f 4)2 = 1+퐞ퟔ+퐟ퟖ-2퐞ퟑ+2퐟 ퟒ-2퐞ퟑ 퐟ퟒ
11. (0.1 + 0.2x − 0.3yz)2 = 0.01+0.04퐱ퟐ+0.09퐲 ퟐ 퐳ퟐ+0.04x-0.06yz-0.12xyz
1
2
13. (
x +
1
3
y −
1
4
)2 =
ퟏ
ퟒ
퐱ퟐ + ퟏ
ퟗ
퐲 ퟐ + ퟏ
ퟏퟔ
+ ퟏ
ퟑ
퐱퐲 − ퟏ
ퟒ
퐱 − ퟏ
ퟔ
퐲
17. (2m + 3n − 4p + 2)2 = 4퐦ퟐ+9퐧ퟐ+16퐩ퟐ+4+12mn-16mp+8m-24np+12n-16p
19. (3a + b − 3c − 3d + e)2 = 9풂ퟐ+풃ퟐ+9풄ퟐ+9풅ퟐ+풆ퟐ+6ab-18ac-18ad+6ae-6bc-6bd+2be+18cd-6ce-6de
EXERCISE 2.4
1. (x+15)(x-15) = 퐱ퟐ − ퟐퟐퟓ
3. (2a+5b)(2a-5b) = ퟒ퐚ퟐ − ퟐퟓ퐛ퟐ
5. (r2s+10t)( r2s-10t) = 퐫ퟒ 퐬ퟐ-100퐭ퟐ
7. (
1
3
+ 2x2y 3)(
1
3
− 2x2y3) =
ퟏ
ퟗ
− ퟒ퐱ퟒ 퐲ퟔ
9. (0.03m2+np2)(0.03m2 − np2 ) = 0.0009퐦ퟒ -퐧ퟐ 퐩ퟒ
11. (x+y-z)(x+y-z) = 퐱ퟐ + 퐲 ퟐ + 퐳ퟐ-2xy-2xz-2yz
13. (a+2b+3c)(a-2b-3c) = 퐚ퟐ − ퟒ퐛ퟐ − ퟏퟐ퐛퐜 − ퟗ퐜ퟐ
15. [2(a + b)2+3(c+d)][2(a + b)2 − 3(c + d)] = 4(퐚 + 퐛)ퟐ-9(퐜 + 퐝)ퟐ

9. EXERCISE 2.5
1. (a+b)(3a+b) = 3퐚ퟐ+4ab+퐛ퟐ
3. (5m-n)(3m+7n) = 15퐦ퟐ+32mn-7퐧ퟐ
5. (r2s)(2r25s) = 2퐫 ퟒ+3퐫 ퟐ퐬-5퐬 ퟐ
7. (0.1x+3)(0.2x-5) = 0.02퐱ퟐ+0.1x-15
9. (
1
2
x+4)(
1
3
x-8) = ퟏ
ퟔ
퐱ퟐ-2
ퟐ
ퟑ
퐱-32
11. (
3
4
p2-3b)(
4
3
p2+5b) = 퐩ퟒ-
ퟏ
ퟒ
퐩ퟐb-15퐛ퟐ
13. (2r+s+t)(2r+s-5t) = 4퐫 ퟐ+4rs-8rt+퐬 ퟐ-4퐬 ퟐ
15. [2(a+b)-3(x+y)][3(a+b)+2(x+y)] = 6퐚ퟐ+12ab-5ax-5ay+6퐛ퟐ-5bx-5by-6퐱ퟐ-12xy-6퐲 ퟐ
EXERCISE 2.6
1. (x + 3y)3 = 퐱ퟑ+9퐱ퟐ 퐲+81x퐲 ퟑ+9퐲 ퟑ
3. (2x2 − 7y)3 = 8퐱ퟔ+84퐱ퟒy-42퐱ퟐ 퐲 ퟐ-343퐲 ퟑ
5. (5a2b − 3y 2)3 = 125퐚ퟔ 퐛ퟑ+45퐚ퟒ 퐛ퟐ 퐲ퟐ-45퐚ퟒ 퐛ퟐ퐲 ퟒ-27퐲 ퟔ
7. (1 − 2a2b3)3 = 1+6퐚ퟐ 퐛ퟑ-14퐚ퟔ 퐛ퟗ
11. (3x+y)(9x2-3xy+y 2) = 27퐱ퟑ+퐲 ퟑ
13. (2a2+5b3)(4a4-10a2b3+25b6) = 8퐚ퟔ+125퐛ퟖ
15. [2x + (a + b)2]3 = 8x+퐚ퟐ 퐛ퟐ

10. CHAPTER 2 TEST
A.
1. (−5x2y3)2 = 25퐱ퟒ 퐲 ퟔ
3. (−
3
4
a2y 3)2 =
ퟗ
ퟏퟔ
퐚ퟒ 퐲ퟔ
5. (0.3m3 + 0.5n)2 = 0.09퐦ퟒ+0.3퐦ퟐn+0.25퐧ퟐ
7. (2a − 3b − 2c)2 = 4퐚ퟐ+9퐛ퟐ+4퐜ퟐ-12ab-8ac+12bc
9. (3x+4y)(3x-4y) = 9퐱ퟐ-16퐲 ퟐ
11. (
1
4
4
3
x+
2)(
1
4
x −
4
3
22) = (ퟏ
ퟒ
)ퟐ- ( ퟒ
ퟑ퐳ퟐ)ퟐ +
ퟏ
ퟏퟔ퐱 ퟐ- 1
ퟕ
ퟗ
퐳ퟒ
13. [2a+(7b+c)][2a-(7b+c)] = 4퐚ퟐ-49퐛ퟐ+14bc+퐜ퟐ
15. (8x+yz2)(7x-9yz2) = 52퐱−ퟐ-2x퐲 ퟐ+7퐱ퟐx-9
17. (2xa+3y b)(5x4-7y b) = 10퐱퐚ퟐ -14x퐲 ퟔb+15퐱ퟑy
19. [(a+b)-3][(a+b)+5] = 퐚ퟐ 퐛ퟐ+2

11. CHAPTER 3: FACTORING
EXERCISE 3. 1
1. 6ab+8bc = 2b(3a+4c)
3. 15x3+-24x2+6x = 3x(5퐱ퟐ+8x+2)
5. 18x3y 3+27x2y 2+-4xy = xy(18퐱ퟐ 퐲ퟐ+27xy-4)
7. 4x2+-8x3+10x4y+-12x5y2 = 2x2(2-4x+5x2y-6x3y2)
9. 24x2(a+b)+-32x3(a+b) = 8퐱ퟐ(a+b)(3-4x)
11. 5a+10b+15c+-20d = 5(a+2b-3c-4d)
15. 14xn−1-21xn−1 = ퟒퟐ퐧+ퟏ
17. 0.5x4-1.5x3+2x2+4.5x = 3퐱ퟐ
19. 36a2b(3x+y)-18ab2(3x+y)+-81ab(3x+y) = 9ab(3x+y)(4a-2b-9)
EXERCISE 3.2
1. 4a2+-25b2 = (2a+5b)(2a+-5b)
3. 49m4n2+100p6 = (100퐩ퟑ+7퐦ퟐn)(-10퐩ퟑ + ퟕ퐦ퟐ )
5. 81x4+-36y 2z4 = 9(3퐱ퟐ+2y퐳ퟐ)(3퐱ퟐ+-2y퐳ퟐ)
7. 4/9 v 2-m2n4 = (2v/3-퐦퐧ퟐ )( 퐦퐧ퟐ+2v/3)
9. 25y 6+-12y 4 = 퐲 ퟒ (-12+25퐲 ퟐ)
11. 1/16x41/25y 2z4 = (y퐳ퟐ + 퐱ퟐ )( 퐱ퟐ-y퐳ퟐ)
13. 9(a + b)2 = (3a+3b-퐜ퟐ퐱) (3a+3b+퐜ퟐ퐱)
15. a2b2-121c 6d4m = (ab-11퐜ퟑ 퐝ퟐ퐦) (ab+11퐜ퟑ 퐝ퟐ퐦)
17. 98x2n-18y 4m = 2(7퐱퐧-3퐲 ퟐ퐦) (7퐱퐧+3퐲 ퟐ퐦)
19. 4x2(a + b)2-y 2z4m = (2ax+2bx-y퐳ퟐm) (2ax+2bx+y퐳ퟐm)

12. EXERCISE 3.3
1. 27x3+y 3 = (3x+y)(9퐱ퟐ-3xy+퐲 ퟐ)
3. 343m3-125n3 = (7m-5n)(48퐦ퟐ+35mn+25퐧ퟐ)
5. 3x4y+-24xy 4 = 3xy(x-2y)( 퐱ퟐ+2xy+4퐲 ퟐ)
7. 54x6+-16y 3 = 2(3퐰ퟐ-2y)(9퐱ퟒ+6퐱ퟐy+4퐲 ퟐ)
9. 0.125v 3-m6n = (0.5v-퐦ퟐ퐧)(0.25퐯 ퟐ+0.5퐦ퟐ퐧v+퐦ퟒ퐧)
15. 8/125a3b3 − c 6 = (2ab/5-퐜ퟐ)(4퐚ퟐ 퐛ퟐ/25+2ab퐜ퟐ/5+퐜ퟒ)
17. a3(m+n)-512 = 퐚ퟑm+퐚ퟑn-512
19. 8a3+27(x + y)3 = (2a+3x+3y)(4퐚ퟐ-6ax-6ay+9퐱ퟐ+18xy+9퐲 ퟐ)
EXERCISE 3.4
1. 4a2+16a+16 = (2a+4)(2a+4)
3. m2+10mn+25n2 = (m+5n)(m+5n)
5. a4+10a2+25 = (퐚ퟐ + ퟓ)( 퐚ퟐ + ퟓ)
7. 2a2+8ab+8b2 = 2(퐚 + ퟐ퐛)ퟐ
9. 4e2+48ef 2+144f 4 = (2e+12퐟ퟐ)(2e+12퐟ퟐ)
11.
1
16
x2-
9
2
ퟏ
ퟒ
x + 81 = (
퐱 − ퟗ)( ퟏ
ퟒ
퐱 − ퟗ)
13. 9a2n+48an bn+64b2n = (3퐚퐧+8퐛퐧) (3퐚퐧+8퐛퐧)
17. 1.44y 6+2.4y 3z2+z4 = (1.2퐲 ퟑ + 퐳ퟑ) (1.2퐲 ퟑ + 퐳ퟑ)
19. 1+30m4n2+225m8n2 = (1+15퐦ퟒ 퐧) (1+15퐦ퟒ 퐧)

13. EXERCISE 3.5
1. x2-8x+7 = (x-1)(x-7)
3. x2-4x-21 = (x+3)(x-7)
5. x2+4x-45 = (x+9)(x-5)
7. x2a+xa-42 = (퐱퐚+7)( 퐱퐚 − ퟔ)
9. 2x2-24x+54 = (2x-6)(x-9)
11. 2x2-11x+5 = (2x+1)(x+5)
13. 7x2-12x-4 = (7x+2)(x-2)
15. 12x2+20x+7 = (6x+7)(2x+1)
17. 13x2-14xy b+1 = (13x퐲 퐛-1)(x퐲 퐛-1)
19. 3x2+10xy b-25y2b = (3x-5퐲 ퟐ)(x+5퐲 퐛)
EXERCISE 3.6
1. 푎5 + 푏5 = (x-7)(x-1)
3. 푥7-128 = (x-2)( 퐱ퟔ+2퐱ퟓ+4퐱ퟒ+8퐱ퟑ+16퐱ퟐ+32x+64)
5. 128푥7-1 = (2x-1)(64퐱ퟔ+32퐱ퟓ+16퐱ퟒ+8퐱ퟑ+4퐱ퟐ+2x+1)
7. 푥5푦5-1 = (xy-1)( 퐱ퟒ 퐲ퟒ+퐱ퟑ 퐲ퟑ+퐱ퟐ 퐲 ퟐ+xy+1)
9.
1
32
ퟏ
ퟐ
+푥5 = (
+x)( ퟏ
+
ퟏퟔ
ퟏ
ퟖ
ퟏ
ퟒ
x+
ퟏ
ퟐ
퐱ퟐ+
퐱ퟑ+퐱ퟒ)
11. 푥9-푦9 = (x-y)( 퐱ퟖ + 퐱ퟕ 퐲 + 퐱ퟔ 퐲 ퟐ + 퐱ퟓ 퐲 ퟑ + 퐱ퟒ 퐲ퟒ + 퐱ퟑ 퐲 ퟓ + 퐱ퟐ 퐲 ퟔ + 퐱퐲 ퟕ + 퐱퐲 ퟖ)
13. 32(푎 + 푏)5-1 = (2a+2b-1)(16퐚ퟒ+64퐚ퟑb+8퐚ퟑ+96퐚ퟐ퐛ퟐ+24퐚ퟐb+4퐚ퟐ+64a퐛ퟑ+24a퐛ퟐ+8ab+2a+16퐛ퟒ+8퐛ퟑ+4퐛ퟐ+2b+1)
15. (푎 + 푏)5-푐5 = 퐚ퟓ 퐛ퟓ − 퐜ퟓ

14. EXERCISE 3.7
1. c 2+3c-cd-3d = (c-d)(c+3)
3. 6a2+9ab-8a-12b = (3a-4)(2a+3b)
5. x2y-yz+2ax2-2az = (y+2a)( 퐱ퟐ-z)
7. 2x2-x+4x-2 = (x+2)(2x-1)
9. ax+bx+ay+by = (x+y)(a+b)
11. 4a2-9b4+2ax-3b2x = 5a퐛ퟐ+a퐱ퟐ
13. 10x2+4xy+45x+18y = (2x+9)(5x+2y)
15. a2+3a-2a-6 = (a+3)(a-2)

15. CHAPTER 4
EXERCISE 4.1
1.
2x
−x
= -2
3. −
1
y
= − ퟏ
퐲
5.
−r
−s−t+u
=
퐫
퐬+퐭−퐮
7.
x−y
y−z
=
퐱
퐳
9.
−3
(5)2(−2)2 =
−ퟑ
ퟐퟗ
EXERCISE 4.2
1.
24x2x4
9x2y2 =
ퟖ
ퟑ퐲 ퟐ
3.
3(y+2)
3(y+4)
=
퐲+ퟏ
퐲+ퟐ
5.
4x2−1
2x+1
= 2x-1
7.
a2+3a−10
a2+a−6
=
퐚+ퟓ
퐚+ퟑ
9.
m3−27
3−m
= 9+3m+퐦ퟐ
11.
a2−6a+8
a2+a−6
=
퐚−ퟒ
퐚+ퟑ
13.
125a3−x3
x−5a
= 25퐚ퟐ − 퐚퐱 + 퐱ퟐ
15.
14a2−31a−10
7a2−33a−10
=
(ퟐ퐚+ퟓ)
(퐚+ퟓ)

16. EXERCISE 4.3
1.
18y2
25z
∙
5z2
3y2 =
ퟔ퐳ퟐ
ퟓ
3.
3y+18
y2 ∙ 4y4
6y+36
= ퟒ퐲 ퟐ
ퟐ
5. w+3 ∙
w
2w2+5w−3
=
퐰
ퟐ퐰−ퟏ
7.
3a2−13a+4
9a2−6a+1
∙
28+7a
a2−16
=
ퟕ(ퟒ+퐚)
(ퟑ퐚−ퟏ)(퐚−ퟒ)
9.
4a+12
6a−18
∙
5a−15
3a+9
=
ퟏퟎ
ퟗ
EXERCISE 4.4
1.
x
2
,
y
6
,
z
9
= 1xyz
3.
a
52
,
r
169
,
s
4
=
퐚
ퟏ
퐫
ퟏ
퐬
ퟒ(ퟓퟐ)(ퟏퟔퟗ)
5.
x
x+y
,
y
x−y
,
xy
x2−y2 =
퐱
ퟏ
퐲
ퟏ
퐱퐲
(퐱−퐲)(퐱+퐲)(퐱 ퟐ−퐲 ퟐ)
7.
2
x2+4x+4
,
3
x+2
,
3
3m−3n
=
ퟐ
ퟏ
ퟑ
ퟏ
ퟒ
(퐱 ퟐ+ퟒ퐱+ퟒ)(퐱+ퟐ)(퐱 ퟐ+ퟐ퐱)
9.
1
x2+4x+4 ,
2
x2+x−20
=
ퟏ
ퟏ
ퟐ
(퐱 ퟐ+퐱−ퟐퟎ)(퐱 ퟐ−퐱−ퟏퟐ)
11.
1
(c−d)2 ,
b
a−b
,
c
a2 − 2ab + b2 =
ퟏ
ퟏ
ퟐ
ퟏ
ퟑ
ퟑ[(퐜−퐝)ퟑ][(퐜−퐝)ퟐ](퐜−퐝)
13.
1
x2+xy
,
2
xy2+y3 =
ퟏ
ퟏ
ퟏ
(퐱퐲 ퟐ+퐲 ퟑ)(퐱ퟐ+퐱퐲)
15.
a
(a−b)2 ,
b
a−b
,
c
a2−2ab+b2 =
퐚
ퟏ
퐛
ퟏ
퐜
[(퐚−퐛)ퟐ](퐚−퐛)(퐚ퟐ−ퟐ퐚퐛+퐛ퟐ)

17. CHAPTER 5: EXPONENTS
EXERCISE 5.1
1. x5 ∙ x3 = 퐱ퟖ
3. (2x2z5)4 = 4퐱ퟖ 퐳ퟐퟎ
5.
18x3y5z3
6xy2z0 = 3퐱ퟐ 퐲 ퟑ퐳ퟑ
7.
(a2b3)2
a3b2 = a퐛ퟒ
9. (−2x2a−1y1−2a)3 = ퟐ퐱ퟐ 퐲 ퟑ
11.
(m−1)3(1)3
m2−m =
퐦ퟐ−ퟐ퐦+ퟏ
퐦+ퟏ
13. [(−2)3]2 ∙ [(−2)2]2 = 65.536
15.
44∙ 36 ∙ (x5)2
2893(x2)3 = 퐱ퟒ
EXERCISE 5.2
1.
x2y−3
x3y−2 =
ퟏ
퐱퐲
3. a3 ∙ 3−2 = 3a
m−2n2
mn−2 ) =
5. (
퐧ퟒ
퐦ퟑ
7.
x−2+x
x−2 = 퐱ퟑ
9. (50x−2)2(23x3)0 =
ퟏ
퐱 ퟒ
11.
a−mma
a2mm−2a =
퐚퐦
퐚ퟐ퐦ퟐ
13.
5−1b−2c0
(2bc)−2 ∙ (
1
a−2b
)−1 =
ퟒ퐛퐜ퟐ
ퟓ퐚ퟐ
a−2m+2bn
a−3m+3b−2n)−2(
15. (
2−2m3
22m4 )0 = 퐚퐦− ퟏ 퐛ퟑ퐧

18. EXERCISE 5.3
1
2 = 5
1. 25
6
5 = 64
3. 32
6
5 = 64
5. 32
1
3 = 2
7. 8
1
3 = 4
9. 64
2
3 = 8
11. [8(푎 + 푦)]
1
2 = 퐱퐲 ퟐ
13. (푥2푦−2)
15.
(4푚2)
(9푛4)
=
ퟐ풎
ퟗ풏ퟐ