प्रश्नावली-3A
1. रिक्त स्थानों की पूर्ति करें-
(a)a3bc-ab3c-abc3=abc(….)
(b) x(a-b)+y(a-b)+z(a-b)=(…)(x+y+z)
(c)9×2+24x+16=(3x+4)(……)
(d)36×2+25+60x=(…..)(6x+5)
(e)a2-25b2=(a+…..)(a-……)
Answer:—–
(a) (a2+b2-c2)
(b) (a-b)
(c) 3x+4
Details:—-
9×2+24x+16
9×2+12x+12x+16
3x(3x+4)+4(3x+4)
(3x+4)(3x+4)
(d) 6x+5
36×2+25+60x
36×2+60x+25
36×2+30x+30x+25
6x(6x+5)+5(6x+5)
(6x+5)(6x+5)
(e) 5b, -5b
a2-25b2
(a)2-(5b)2=(a+5b)(a-5b)
2. गुणनखण्ड निकाले-
(a)4y2-4y+1
4y2-2y-2y+1
2y(2y-1)-1(2y-1)
(2y-1)(2y-1)
(b)9a2+60a+100
9a2+30a+30a+100
3a(3a+10)+10(3a+10)
(3a+10)(3a+10)
(c) 49a2+70ab+25b2
49a2+35ab+35ab+25b2
7a(7a+5b)+5b(7a+5b)
(7a+5b)(7a+5b)
(d)144y2+24y+1
144y2+12y+12y+1
12y(12y+1)+1(12y+1)
(12y+1)(12y+1)
(e) 25×2+ 10 x+ 1
9 81
25×2+ 5x + 5x + 1
9 9
5x(5x+ 1 )+ 1 (5x+ 1 )
9 9 9
(5x+ 1 )(5x+ 1 )
9 9
3. गुणनखण्ड करें—
(a) 4a2-9b2
(2a)2-(3b)2
(2a+3b)(2a-3b)
(b)100-9×2
(10)2-(3x)2
(10+3x)(10-3x)
(c)1-4×2
(1)2-(2x)2
(1+2x)(1-2x)
(d) 1 x2 – 1 y2
4 81
( 1 x)2 – ( 1 y)2
2 9
( 1 x + 1 y)( 1 x – 1 y)
2 9 2 9
(e) 25×2 – y2
4 9
( 5x )2 – ( y )2
2 3
( 5x + y ) ( 5x – y )
2 3 2 3
(f) x2 – (y+z)2
(x+y+z)(x-y-z)
4. गुणनखण्ड ज्ञात करें-
(a)(x+y)2+2(x+y)(x-y)+(x-y)2
(x+y+x-y)2=(2x)2=4×2
(b)9(x-2y)2+36(x-2y)(x+y)+36(x+y)2
{3(x-2y)2+2×3(x-2y)×6(x+y)+{6(x+y)}2
{3(x-2y)+6(x+y)}2=(3x-6y+6x+6y)2
(9x)2=81×2
5. गुणनखण्ड ज्ञात करें-
(a)(x+y)2-2(x+y)(x-y)+(x-y)2
{(x+y)-(x-y)}2=(x+you+y)2
(2y)2=4y2
(b) 9(x+y)2-12(x2-y2)+5(x-y)2
{3(x+y)}2-2×3(x+y)×2(x-y)+{2(x-y)}2
{3(x+y)-{2(x-y)}2
(3x+3y-2x+2y)2=(x+5y)2
(x+5y)(x+5y)
6. गुणनखण्ड ज्ञात करें-
(a) 4a2-9(b+c)2
(2a)2-{3(b+c)}2
(2a+3b+3c)(2a-3b-3c)
(b)2×2-18y2
2(x2-9y2)
2{(x)2-(3y)2}=2{(x+3y)(x-3y)}
2(x+3y)(x-3y)
(c) 50b2c2-98a2
2(25b2c2-49a2)
2(5bc)2-(7a)2
2(5bc+7a)(5bc-7a)
(d)3×3-243xy2
3x(x2-81y2)
3x{(x)2-(9y)2}
3x(x+9y)(x-9y)
(e)x5 – x3
x3(x2-1)
x3{(x)2-(1)2}
x3(x+1)(x-1)
(f) x3-x
x(x2-1)
x{(x)2-(1)2}
x(x+1)(x-1)
7.गुणनखण्ड ज्ञात करें-
(a) 1-(a2+b2)+2ab
(1)2-(a+b)2
(1+a+b)(1-a-b)
(b) b2+c2+2(ab+bc+ca)
b2+c2+2ab+2bc+2ca
b2+c2+2bc+2a(b+c)
(b+c)2+2a(b+c)
(b+c)(b+c+2a)
(c)25×2-10x+1-36y2
(5x)2-2×5x×1+(1)2-36y2
(5x-1)2-(6y)2
(5x-1+6y)(5x-1-6y)
(d)x2+y2+6y-9
x2-(y2-6y+9)
x2-(y2+2×y×3+(3)2)=x2-(y-3)2
(x+y-3)(x-y+3)
8.गुणनखण्ड ज्ञात करें-
(i)4×2+y2+z2-4xy-2yz+4xz
(2x)2+(-y)2+(z)2+2×2x×(-y)+2×(-y)×z+2×z×x
(2x-y+z)2=(2x-y+z)(2x-y+z)
(ii)4×2+9y2+16z2+12xy-24yz-16xz
(2x)2+(3y)2+(-4z)2+2×2x×3y+2×3y×(-4z)+2×(-4z)×(2x)
(2x+3y-4z)2=(2x+3y-4z)(2x+3y-4z)
(iii)x2+4y2+z2+4xy-4yz-2zx
(x)2+(2y)2+(-z)2+2×x×2y+2×2y×(-z)+2×(-z)×x
(x+2y-z)2=(x+2y-z)(x+2y-z)
(iv) 4×2+9y2+4z2-12xy-12yz+8xz
(-2x)2+(3y)2+(-2z)2+2×(-2x)×3y+2×3y×(-2z)+2×(-2z)×(-2x)
=(-2x+3y-2z)2=(-2x+3y-2z)(-2x+3y-2z)
(v) 1 x2+y2+ 1 z2-xy- 1 yz+ 1 zx
4 16 2 4
( 1 x)2+(-y)2+( 1 z)2+2× 1 x×(-y)
2 4 2
+2×(-y)× 1 z+ 2× 1 z× 1 x
4 4 2
=( 1 x-y+ 1 z) 2
2 4
=( 1 x-y+ 1 z)( 1 x-y+ 1 z)
2 4 2 4
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