प्रश्नावली-8A
1. निम्नलिखित का विभाजन कीजिए-
(a)42a÷7
=6a×7÷7=6a
(b)72x2y÷(-9xy)
= 8×9×x×x×y
-9xy
=-8x
(c)-68abc÷17b
= -4×17abc
17b
=-4ac
(d)38a3b2c÷57ab2c
= 2×19×a×a×a×b×b×c
3×19×a×b×b×c
= 2a2
3
(e)21x4y7÷(-14x2y5)
= 7×3×x2×x2×y2×y5
-7×2×x2×y5
= -3x2y2
2
(f) -24m2n4p3÷16mn2p3
= -24m×n2×n2×p3
16×m×n2×p3
= -3mn2
2
2. भाग दीजिये—-
(a)(9y2-6y)÷3y
=3y(3y-2)÷3y=(3y-2)
(b)(4m3-26m2+6m)÷4m
=2m(2m2-13m+3)÷4m
=(2m2-13m+3)÷2
= 2m2-13m+3 =m2- 13m + 3
2 2 2
(c)(8a3b2-6a2b3+7a2b2)÷(-a2b2)
=a2b2(8a-6b+7)÷(-a2b2)
=-(8a-6b+7)=(-8a+6b-7)
(d)(21x2yz-36xy2z-45xyz2)÷3xyz
=3xyz(7x-12y-15z)÷3xyz
=7x-12y-15z
(e)(24pqr-36pq-48qr)÷(-12q)
=12q(2pr-3p-4r)÷(-12q)
=-(2pr-3p-4r)=-2pr+3p+4r
(f)
(44a3b7-121a8b5+33a6b3)÷(22a3b3)
= 44a3b7-121a8b5+33a6b3
22a3b3
= 44a3b7 – 121a8b5 + 33a6b3
22a3b3 22a3b3 22a3b3
=2b4 – 11 a5b2 + 3 a3
2 2
3. भाग दीजिये—
(a)8(3x+4y)(x-7y)÷(x-7y)
=8(3x+4y)
(b)39(6x-5y)(3x+2y)÷26(6x-5y)
= 39(6x-5y) (3x+2y)
26(6x-5y)
= 3 (3x+2y)
2
(c)-48x3y3(5x-2y)(6x-y)÷36x2y(6x-y)
= -48x3y3(5x-2y) (6x-y)
36x2y(6x-y)
= -4 xy2
3
(d)
27m2n3(4m-2n)(6m+7n)÷54(4m-2n)
= 27m2n3(4m-2n)(6m+27n)
54(4m-2n)
= (6m+7n)m2n3
2
4. भाग दीजिये-
(a)(12x-15y)÷(4x-5y)
=3(4x-5y)÷(4x-5y)=3
(b)(32×2-8xy)÷x(4x-y)
=8x(4x-y)÷x(4x-y)=8
(c)35a2b2(6a-9b)÷15ab(2a-3b)
= 35a2b2×3(2a-9b)
15ab(2a-3b)
=7ab
(d)
72abc(8a-6b)(9a+6b)÷81bc(4a-3b)(3a+2b)
= 72abc×2(4a-3b)×3(3a+2b)
81bc(4a-3b)(3a+2b)
= 16a
3
5. गुणनखण्ड विधि द्वारा ज्ञात कीजिए-
(a)(a2 – 81)÷(a-9)
={(a)2 – (9)2}÷(a-9)
=(a+9)(a-9)÷(a-9)=(a+9)
(b)(4×2 – 25)÷(2x+5)
={(2x)2-(5)2}÷(2x+5)
=(2x+5)(2x-5)÷(2x+5)=(2x-5)
(c)(16×4 – y4)÷(2x-y)
={(4×2)2-(y2)2}÷(2x-y)
={(4×2+y2)(4×2 – y2)}÷(2x-y)
=(4×2+y2){(2x)2-(y)2}÷(2x-y)
=(4×2+y2)(2x+y)(2x-y)÷(2x-y)
=(4×2+y2)(2x+y)
(d)(3p2-6pq+3q2)÷(p-q)
=3(p2-2pq+q2)÷(p-q)
=3{(p)2-2×p×q+(q)2}÷(p-q)
=3(p-q)2÷(p-q)
=3(p-q)=3p-3q
(e) (9×2+24xy+16y2)÷(3x+4y)
={(3x)2+2×3x×4y+(4y)2}÷(3x+4y)
=(3x+4y)2÷(3x+4y)
=(3x+4y)
(f)(5a2-55a+150)÷(a-6)
=5(a2-11a+30)÷(a-6)
=5{a2-6a-5a+30)÷(a-6)
=5{a(a-6)-5(a-6)}÷(a-6)
=5(a-6)(a-5)÷(a-6)
=5(a-5)=5a-25
(g)(x2-17x-38)÷(x+2)
=(x2-19x+2x-38)÷(x+2)
={x(x-19)+2(x-19)}÷(x+2)
=(x-19)(x+2)÷(x+2)=(x-19)
(h)15abc(3a2-57a+144)÷9b(a-16)
=15abc×3(a2-19a+48)÷9b(a-16)
=15abc×3{a2-16a-3a+48)÷9b(a-16)
=15abc×3{a(a-16)-3(a-16)}÷9b(a-16)
=15abc×3(a-3)(a-16)÷9b(a-16)
=5ac(a-3)
6. साधारण विधि से भाग दीजिये-
(a)(18×2 – 2y2)÷(3x+y)
3x+y) 18×2 – 2y2(6x-2y
18×2 – 6y2
6xy-2y2
6xy-2y2
X
(b)(16m2-40mn+25n2)÷(4m-5n)
4m-5n)16m2-40mn+25n2(4m-5n
16m2-20mn
-20mn + 25n2
-20mn + 25n2
X
(c)(8×2+22x-21)÷(2x+7)
2x+7)8×2+22x-21(4x-3
8×2+28x
-6x-21
-6x-21
X
(d)(-4x+32×2 – 21)÷(8x-7)
8x-7)32×2-4x-21(4x+3
32×2-28x
24x-21
24x-21
X
(e)(19a-56+132a2)÷(8+11a)
8+11a)19a-56+132a2(-7+12a
-77a -56
96a+132a2
96a+132a2
X
(f)(12x+16×2-108)÷(9-4x)
9-4x)12x+16×2 -108(-4x-12
-36x+16×2
48x-108
48x-108
X
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