प्रश्नावली-7B
1. निम्नलिखित में प्रत्येक एकपदी युग्मों का गुणनफल ज्ञात कीजिए—-
(i)3, 4x
=3×4x=12x
(ii)-2a, 4b
=2a×4b=-8ab
(iii)4×3, -8x
=4×3×(-8x)=-32×4
(iv)0, 3y
=0×3y=0
2. निम्नलिखित प्रत्येक युग्म में आयत की लंबाई तथा चौड़ाई को सूचित किया गया है, प्रत्येक में आयत का क्षेत्रफल ज्ञात कीजिए-
(i)a, b
a×b=ab
(ii)10x, 4y
10x×4y=40xy
(iii)24×2, 3xy
24×2×3xy=72x3y
(iv)4mn, 7mnp
4mn×7mnp=28m2n2p
(v)20×2, 4y2
20×2×4y2=80x2y2
(vi)14abc, 3a2b
14abc×3a2b=42a3b2c
3. ऐसे घनाभों का आयतन ज्ञात कीजिए जिनकी लंबाई, चौड़ाई और ऊंचाई क्रमशः निम्नलिखित हैं—
(i)5x, 3×2, 8×4
5x×3×2×8×4=120×7
(ii)2a, 8b, 4c
2a×8b×4c=64abc
(iii)ab, 3a2b, 4ab2
ab×3a2b×4ab2=12a4b4
(iv)3xyz, 7xy2z, 8x2yz
=3xyz×7xy2z×8x2yz=168x4y4z3
(v)a2b2c2, 3a2bc3, 4abc
=a2b2c2×3a2bc3×4abc=12a5b4c6
4. निम्नलिखित प्रत्येक व्यंजक को सरल कीजिए और अज्ञात राशि के दिए गए के लिए दिए गए व्यंजक का मान निकालिए-
(i)a(2a-4)+9, a=3
=3(2×3-4)+9
=3(6-4)+9
=3×2+9=6+9=15
(ii)(a+3b)7-2a-12b, a=4, b=-2
=[(4+3×(-2)]×7 – 2×4 -12×(-2)
=(4-6)×7- 8 + 24=-2×7-8+24
=-14-8+24=-22+24=2
(iii) x(4x-7)+3(x+6)-12x, x=7
=7(4×7-7)+3(7+6)-12×7
=7(28-7)+3(7+6)-84
=7×21+3×13-84
=147+39-84=102
(iv) x(3x-4)+4(x-7)+x(3-2x), x=4
=4(3×4-4)+4(4-7)+4(3-2×4)
=4(12-4)+4×(-3)+4(3-8)
=4×8-12+4×(-5)
=32-12-20=0
5. योगफल ज्ञात कीजिए-
(i)4a(8-3a), 7a2-4a+6
=4a(8-3a)+7a2-4a+6
=32a-12a2+7a2-4a+6
=-12a2+7a2+32a-4a+6
=-5a2+28a+6
(ii) 3x(4×2-5x+3), 2(x3-9x+6)
=3x(4×2-5x+3)+2(x3-9x+6)
=12×3-15×2+9x+2×3-18x+12
=14×3-15×2-15x+12
(iii)8a(3a-2b+7c), 7b(a-3b+2c), c(a+b-5c)
=8a(3a-2b+7c)+7b(a-3b+2c)+c(a+b-5c)
=24a2-16ab+56ac+7ab-21b2+14bc+ac+bc-5c2
=24a2-21b2-5c2-16ab+7ab+56ac+ac+14bc+bc
=24a2-21b2-5c2-9ab+57ac+15a
(iv)3p(-p+2q-3r),5q(4p-7q+r),6r(p+2q+4r)
=3p(-p+2q-3r)+5q(4p-7q+r)+6r(p+2q+4r)
=-3p2+6pq-9r2+20pq-35q2+5qr+6pr+12qr+24r2
=-3p2-35q2+24r2-3rp+26pq+17rq
6.(i)2a(3a-b+c), 4a(2a+b-7c)
=2a(3a-b+c)-4a(2a+b-7c)
=6a2-2ab+2ac-8a2-4ab+28ac
=-2a2-6ab+30ac
(ii)4x(2x-y+5z), 3y(4x-2y+7z)
=4x(2x-y+5z)+3y(4x-2y+7z)
=8×2-4xy+20zx+12xy-6y2+21yz
=8×2-16xy-6y2+20zx-21yz
(iii)5l(l-m+2p), 7p(l-p+m)
=5l(l-m+2p)+7p(l-p+m)
=5l2-5ml+10lp+7pl-7p2+7mp
=5l2+7p2-5lm+3lp-7mp
(iv)
3a(2b+c)-4(a+b)c,4a(a+b+c)-2b(a+b-c)
=3a(2b+c)-4(a+b)c-[4a(a+b+c)-2b(a+b-c)]
=6ab+3ac-4ac-4bc-[4a2+4ab+4ac-2ab-2b2+2bc]
=6ab+3ac-4ac-4bc-4a2-4ab-4ac+2ab+2b2-2bc
=-4a2+2b2+4ab-5ac-6bc
7. गुणा कीजिए—
(i)(7a+5)×(2a+b)
=7a×2a+7a×b+5×2a+5×b
=14a2+7ab+10a+5b
(ii)(2x+4y)×(4x-7y)
=2x×4x+2x×(-7y)+4y×4x+4y×(-7y)
=8×2-14xy+16xy-28y2
=8×2+2xy-28y2
(iii)(8p-2q)×(3p-6q)
=8p×3p+8p×(-6q)-2q×3p-2q×(-6q)
=24p2-48pq-6pq+12q2
=24p2-54pq+12q2
(iv)(2a2+7b2)×(4a-5b)
=2a2×4a+2a2×(-5b)+7b2×4a+7b2×(-5b)
=8a3-10a2b+28ab2-35b3
(v)(5x+2y)×(x-2y+3z)
=5x×x+5x×(-2y)+5x×3z+2y×x+2y×(-2y)+2y×3z
=5×2-10xy+15xz+2xy-4y2+6yz
=5×2-4y2-8xy+15xz+6yz
(vi)(3a-5b)×(-a-b+7c)
=3a×(-a)+3a×(-b)+3a×7c-5b×(-a)-5b×(-b)-5b×7c
=-3a2-3ab+21ac+5ab+5b2-35bc
=-3a2+2ab+5b2+21ac-35bc
(vii)(2a-3b+4c)×(a+5b-6c)
=2a×a+2a×5b+2a×(-6c)-3b×a-3b×5b-3b×(-6c)+4c×(-6c)
=2a2+10ab-12ac-3ab+15b2-3bc-24c2
=2a2-15b2-24c2+7ab-8ac+38bc
8. सरल कीजिए-
(i)(3a+2b)(4a-b+3c)+(5a-2b)c
=3a×4a+3a×(-b)+3a×3c+2b×4a+2b×(-b)+2b×3c+5a×c-2b×c
=12a2-3ab+9ac+8ab-2b2+6bc+5ac-2bc
=12a2+5ab+14ac+4bc-2b2
(ii)(x2 – 6)(x+4)+16
=x2×x+x2×4-6x-6×4+16
=x3+4×2-6x-24+16=x3+4×2-6x-8
(iii)(p+q2)(p2-q2)
=p×p2+p×(-q2)+q2×p2+q2×(-q2)
=p3-pq2+p2q2-q3
(iv)(x+y)(u-v)+(x-y)(u+v)+2(xu-yv)
=xu-vx+yu-vy+xu+vx-yu-yv+2xu-2vy
=2xu-2yv+2xu-2yv
=4xu-4yv
(v)(s+t)(3s+2t)+(3s-t)(s-4t)
=3s2+2st+3st+2t2+3s2-12ts-st+4t2
=3s2+3s2+2st+3st-12st-st+2t2+4t2
=6s2-8st+6t2
(vi)(p+q)(p2-pq+q2)-p3
=p3-p2q+q2p+qp2-pq2+q3-p3
=q3
(vii)(2.5a-3b)(2a+b)+3(a+1.5ab)
=2.5a×2a+2.5a×b-3b×2a-3b×b+3×a+3×1.5ab
=5a2+2.5ab-6ab-3b2+3a+4.5ab
=5a2-3b2+3a+ab
(viii)(1.2x-0.5y)(1.2x+0.5y)-1.75y2
=1.2x×1.2x+1.2x×0.5y-0.5y×1.2x-0.5y×0.5y-1.75y2
=1.44×2+0.6xy-0.6xy-0.25y2-1.75y2
=1.44×2-0.25y2-1.75y2
=1.44×2-2y2
(ix) (4x-2y)(16×2+8xy+4y2)
=4x×16×2+4x×8xy+4x×4y2-2y×16×2-2y×8xy-2y×4y2
=64×3+32x2y+16xy2-32x2y-16xy2-8y3
=64×3-8y3
(x) (a+b+c)(a2+b2+c2)-ab(a+b+c)-bc(a+b+c)-ac(a+b+c)
=a3+ab2+ac2+a2b+b3+bc2+a2c+b2c+c3++b+c-a2b-ab2-abc-abc-b2c-bc2-a2c-abc-ac2
=a3+b3+c3-3abc
9. नीचे दिए गए गुणन सारणी को भरिए-
× 3a 2b -4c 2ab 7a2b
-8a -24a2 -16ab 32ac -16a2b -56a3b
3b 9ab 6b2 -12bc 6ab2 21a2b2
7c 21ac 14bc -28c2 4abc 49a2bc
-4ab -12a2b -8ab2 16abc 8a2b2 -28a3b2
a2b2 3a3b2 2a2b3 -4a2b2c 2a3b3 7a4b3
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