f) 8 a^4 12 a^3 b+2a^2 b^2 +3ab^3 b^4
g) 9 x^2 + 6xy 3 y^2
h) 5 x^2 6 xy 2 y^2
i) x 122 + 127 +x^32
j) x 32 +^103 x^82
k) 10 x 12 y
l) 2 a^2 + 3ab+ 2a+ 3b- 4
5. 4- a) 5
b)k= 3 ork= 1
c)k < 0
d)k > 4 - a)x^2 + 8 +x^162
b) 6 - a)a^2 + 2 +a^12
b) 9
c) 13- a) 9 y^2 + 3 + 4 y^12
b) 16 - a)a^2 +^23 + 9 a^12
b)a^3 + 271 a 3
c) 6
Exercise 1 – 5:
1.4(3x+ 8y)
2. 2 ab(b+ 2a)- 3 b(6a c)
- 6 k(2j+ 3q)
- 12 a( 1 + 2a^2 )
6. 2 a(b+ 4)- 8 kj(3 2 k)
8. ab(a+b) - 18 b^2 q(4 bq)
10.5(5x^3 y)(5x^3 +y) - 2 x(3x+ 1 + 5x^2 )
12.xy(2y+yz+ 3) - 12 k^2 j(1 + 2j)
14.3(a^2 + 2a 6) - 7 a+ 4
Exercise 1 – 6:
1.(y 3)(4 k)
2.(a 1)(a 5)(a+ 5)
3.(b+ 4)(m)(b 6)
4.(a+ 7)(a^2 + 9)
5.(b 4)(3b+ 7)
6.(z+ 6)(3g+ 2)
7.(y+ 2)(4b+ 5)8.(r+ 5)(3d+ 14)
9.(6x+y 3)(6x+y+ 3)
10.3(2x y)(3y 2 x)
11.(4a+ 3b+ 4c)(4a 3 b 4 c)
12.( 2 b+ 11)(4b 19)
13.(29 26 a)(30a 41)
14.(4k 2)(4k+ 2)15.(abc 1)(abc+ 1)
16.
( 1
3 a ^2 b) ( 1
3 a+ 2b)- 2 (^12 x+ 1) (^12 x 1 )
18.(y
p
8)(y+
p
8)
19.(y
p
13)(y+
p
13)
20.(a 3 b)(a 5 b)(a+ 3b)^2
Exercise 1 – 7:
1.(2d 3 r)(3 +t^5 )
2.(z 2 m)(9 +b^3 )
3.(7z 2 y)(5 +c^5 )
4.(3 +a)(2x+ 1)
5.(x+ 5)(x 6)
6.(5 a)(x+ 2y)7.(a x)(a 2)
8.(y+ 2)(5x 3)
9.( a+b)(a+ 1)
10.(7m 2 n)(2 +j)
11.(7r 5 x)(4 +g)
12.(5d 3 m)(5 +y)13.(5q 2 z)(9 +c)
14.(2j 5 v)(3 +y)
15.(2a 5 k)(8 +z)
16.(a b)(x+y+ 2)
17.(3a+b)(x y 3)Exercise 1 – 8:
1.(x+ 5)(x+ 3)
2.(x+ 8)(x+ 1)
3.(x+ 6)^2
4.(h+ 3)(2h 1)
5.(x+ 1)(3x+ 1)
6.(s+ 2)(3s 5)
7.(x+ 3)(x 5)
8.(x+ 3)(x 1)
9.(x+ 5)(x 4)10.(x 5)(x+ 4)
11.2(x+ 1)(x+ 10)- 2 (a+ 1) (3a+ 4)
- 3 (2v 3) (v 3)
- 3 (g 3) (2g+ 1)
15.(3x+ 1)(x+ 6)
16.(3x 1)(x+ 6)
17.(7x+ 1)(x 1)
18.3(2x+ 1)(x 3)
19.(a 4 b)(a 3 b)
20.(3a 4 b)(a+ 3b)
21.2((7x+ 2)(7x 1))
22.(x 6)(x 5)
23.(a 7)(a 1)
24.(y 3)(y+ 6)
25.3(b+ 4)(b+ 1)
26.6(a+ 7)(a 4)Exercise 1 – 9:
1.(w 2 )(w^2 + 2 w+ 4)
2.(g+ 4 )(g^2 4 g+ 16)
3.(h+ 1 )(h^2 h+ 1)
4.(x+ 2)(x^2 2 x+ 4)
5.(3 m)(9 + 3m+m^2 )
6.2(x y)(x^2 +xy+y^2 )
7.3(k+ 3q)(k^2 3 kq+ 9q^2 )
8.(4t 1)(16t^2 + 4t+ 1)
9.(8x 1)(8x+ 1)
10.(5x+ 1)(25x^2 5 x+ 1)11.(^3
p
25 x+ 1)((^3
p
25)^2 x^2 ^3
p
25 x+ 1)
12.(z)(1 5 z)(1 + 5z+ 25z^2 )
13.(2m^2 +n^3 )(4m^4 2 m^2 n^3 +n^6 )
14.(6n k)(36n^2 + 6nk+k^2 )
15.(5s+d)(25s^2 5 sd+d^2 )
16.(2k+r)(4k^2 2 kr+r^2 )
17.(2jkl b)(4j^2 k^2 l^2 + 2jklabc+b^2 )
18.(3xy+w)(9x^2 y^2 3 xyw+w^2 )
19.2(4m+f)(16m^2 4 mf+f^2 )
20.(p^5 ^12 y^4 ) (p^10 +^12 p^5 y^4 +^14 y^8 )21.(^3 t s)(t^92 +^3 ts+s^2 )
22.( 41 q h)( 161 q 2 + 4 hq+h^2 )23.^13 (6g+v)(36g^2 6 gv+v^2 )
24.(1 x+y)(1 x+y+x^2 2 xy+y^2 )
25.(h 1)(h+1)(h^2 +1)(2g^2 +h)(4g^4
2 g^2 h+h^2 )
26.(x+y)(5w h)(25w^2 + 5wh+h^2 )
27.(x 6)(x+ 1)(3p+w)(9p^2 3 pw+
w^2 )
Exercise 1 – 10:
498 Solutions