From De La Salle Araneta University

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