विविध प्रश्नावली-8
1. गुणनखण्ड कीजिए-
(a)-48pq2+64p3q
=16pq(-3q+4q2)
(b)6x2y2z-9x2y3z4
=3x2y2z(2x-3yz3)
(c)ab-4a+3b-12
=a(b-4)+3(b-4)
=(a+3)(b-4)
(d)xy-20y+4y2-5x
=xy-5x-20y+4y2
=x(y-5)+4y(-5+y)
=(y-5)(x+4y)
(e)27×2+126xy+147y2
=3(9×2+42xy+49y2)
=3{(3x)2+2×3x×7y+(7y)2}
=3(3x+7y)2=3(3x+7y)(3x+7y)
(f)32a2 – 144ab +162b2
=2(16a2-72ab+81b2)
=2{(4a)2-2×4a×9b+(9b)2}
=2(4a-9b)2
(g)49m2 – 16n2
=(7m)2 – (4n)2
=(7m+4n)(7m-4n)
(h)243a2 – 75b2
=3(81a2 – 25b2)
=3{(9a)2 – (5b)2}
=3(9a+5b)(9a-5b)
(i)x4 – 81
=(x2)2-(9)2
=(x2+9)(x2-9)
=(x2+9){(x)2-(3)2}
=(x2+9)(x+3)(x-3)
(j)16a4 – (b+c)4
=(4a2)2 -{(b+c)2}2
={(2a)2}2 – {(b+c)2}2
={(2a)2-(b+c)2}{(2a)2+(b+c)2}
={(2a-(b+c)}{2a+(b+c)}{(2a)2+(b+c)2}
=(2a-b-c)(2a+b+c)(4a2+b2+c2+2bc)
(k)(3m+2n)4 – (3m-2n)4
={(3m+2n)2}2 – {(3m-2n)2}2
={(3m+2n)2+(3m-2n)2}{(3m-2n)2 – (3m-2n)2}
={9m2+4n2+12mn+9m2+4n2-12mn}{(3m+2n)+(3m-2n)}{(3m+2n)(3m-2n)}
=(18m2+8n2)(6m)(4n)
=2(9m2+4n2)6m×4n
=48mn(9m2+4n2)
(l)p2+20p+96
=(p)2+2×p×10+(10)2 -(10)2+ 96
={(p)2+2×p×10+(10)2}-100+96
=(p+10)2 -4=(p+10)2 – (2)2
=(p+10-2)(p+10+2)
=(p+8)(p+12)
(m)a2 -20a +51
=a2 -20a+100 -49
={(a)2-2×10×a+(10)2}-(7)2
={(a-10)2} – (7)2
=(a-10-7)(a-10+7)
=(a-17)(a-3)
(n)x2+19x-120
=x2+24x-5x-120
=x(x+24)-5(x+24)
=(x-5)(x+24)
(o)4y2+56y-128
=(4y2+56y+196)-324
={(2y)2+2×2y×14+(14)2 -324
=(2y+14)2-(18)2
=(2y+14-18)2y+14+18)
=(2y-4)(2y+32)
=2(y-2)(y+16)
2. भाग दीजिये-
(a)(27x4y2-24x2y3+81x2y4)÷9xy2
= 27x4y2-24x2y3+81x2y4
9xy2
= 27x4y2 – 24x2y3 + 81x2y4
9xy2 9xy2 9xy2
=3×3 – 8 xy + 9y3
3
(b)49(4a-6b)(9a+12)÷42(2a-3b)(3a+4)
= 49×2(2a-3b)×3(3a+4) =7
42(2a-3b)(3a+4)
(c)(8a2 – 72)÷(a+3)
=8(a2-9)÷(a+3)
=8{(a)2-(3)2}÷(a+3)
=8(a+3)(a-3)÷(a+3)
=8(a-3)
(d)(18×2 -36xy+18y2)÷3(x-y)
=18(x2-2xy+y2)÷3(x-y)
=18{(x)2-2×x×y+(y)2}÷3(x-y)
=18(x-y)2÷3(x-y)
=6(x-y)
(e)(3a2 -51a -114)÷(a+2)
=3(a2-17a-38)÷(a+2)
=3{a2 -19a + 2a -38}÷(a+2)
=3{a(a-19)+2(a-19)}÷(a+2)
=3(a+2)(a-19)÷(a+2)
=3(a-19)
3. साधारण विधि से भाग दीजिये-
(a)(8×2 +8x -30)÷(2x-3)
2x-3) 8×2+8c-30(4x+10
8×2 -12x
20x-30
20x-30
X
(b) (9a2+2a-7)÷(a+1)
a+1) 9a2 + 2a -7(9a-7
9a2 +9a
-7a-7
-7a-7
X
(c)(24x+32×2 -216)÷(2x+6)
2x+6)24x+32×2 – 216(16x-36
96x+32×2
-72x-216
-72x-216
X
(d)(6-27p+12p2)÷(p-2)
p-2) 6-27p+12p2(-3+12p
6-3p
-24p+ 12p2
-24p2+12p2
X
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