Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड
Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड
बहुपद के गुणनखंड
प्रश्नावली 3 A
- रिक्त स्थानों को भरे-
(a) a3bc − ab3c − abc3 = abc(…. )
हल: a3bc − ab3c − abc3 = abc(a2−b2−c2 )
(b) x(a − b) + y(a − b) + z(a − b) = (…. )(x + y + z)
हल: x(a − b) + y(a − b) + z(a − b) = (a−b )(x + y + z)
(c) 9x2 − 24x + 16 = (3x − 4)(…. )
हल: 9x2 − 24x + 16 = (3x − 4)( 3x – 4 )
(d) 36x2 + 25 + 60x = (…. . )(6x + 5)
हल: 36x2 + 25 + 60x = (6x + 5)(6x + 5)
(e) a2 − 25b2 = (a +……)(a −…. )
हल: a2 − 25b2= (a)2−(5b)2
= (a + 5b )(a −5b )
Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड
- गुणनखंड निकाले-
(i) 4y2 − 4y + 1
हल:
यहाँ,
4y2 − 4y + 1
= (2y)2 – 22y1+(1)2
=(2y+1)2
=(2y+1)(2y+1)
(ii) 9a2 + 60a + 100
हल:
यहाँ,
9a2 + 60a + 100
= (3a)2 – 23a10+(10)2
=(3a+10)2
=(3a+10)(3a+10)
(iii) 49a2 + 70ab + 25b2
हल:
यहाँ,
49a2 + 70ab + 25b2
= (7a)2 – 27a5b+(5b)2
=(7a+5b)2
=(7a+5b)(7a+5b)
Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड
(iv) 144y2 + 24y + 1
हल:
यहाँ,
144y2 + 24y + 1
= (12y)2 – 2712y1+(1)2
=(12y+1)2
=(12y+1) (12y+1)
(v) 25x2 + x +109181 ef
हल:
-
गुणनखंड निकाले-
(i)4a2 − 9b2
हल:
यहाँ,
4a2 − 9b2
= (2a)2 –(3b)2
=(2a+3b) (2a – 3b)
(ii)100 − 9x2
हल:
यहाँ,
100 − 9x2
= (10)2 – (3x)2
=(10+3x) (10 – 3x)
(iii)1 − 4x2
हल:
यहाँ,
1 − 4x2
= (1)2 – (2x)2
=(1+2x) (1 – 2x)
Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड
(iv)x2 − y21
हल:
(v)4
1
81
x2 −
25
4
y2
9
(vi) x2 − (y + z)2
हल:
यहाँ,
x2 − (y + z)2
= (x)2 – (y + z)2
= (x + y + z) [x – (y + z)]
= (x + y + z) (x – y – z)
-
गुणनखंड ज्ञात कीजिये-
(a) (x + y)2 + 2(x + y)(x − y) + (x − y)2
हल:
यहाँ,
(x + y)2 + 2(x + y)(x − y) + (x − y)2
=(x + y)2 + 2 (x + y)(x − y) + (x − y)2
=(x + y + x − y)2
=(2x)2
=4x2
(b) 9(x − 2y)2 + 36(x − 2y)(x + y) + 36(x + y)2
हल:
यहाँ,
9(x − 2y)2 + 36(x − 2y)(x + y) + 36(x + y)2
={3(x − 2y)}2 + 23(x − 2y)6(x + y) + {6(x + y)}2
={3(x − 2y) + 6(x + y)}2
={3x – 6y + 6x + 6y}2
=(9x)2
=81x2
- गुणनखंड ज्ञात कीजिये-
(a) (x + y)2 − 2(x + y)(x − y) + (x − y)2
हल:
यहाँ,
(x + y)2 − 2(x + y)(x − y) + (x − y)2
=(x + y)2 − 2 (x + y)(x − y) + (x − y)2
={x + y – (x − y)}2
=(x + y – x + y)2
=(2y)2
=4y2
(b) 9(x + y)2 − 12(x2 − y2) + 4(x − y)2
हल:
यहाँ,
9(x + y)2 − 12(x2 − y2) + 4(x − y)2
=9(x + y)2 – 12(x + y)(x − y) + 4(x − y)2
={3(x + y)}2 − 23(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)
Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड
- गुणनखंड निकाले-
(a) 4a2 − 9(b + c)2
हल:
यहाँ,
4a2 − 9(b + c)2
= (2a)2 – {3(b + c)}2
= (2a)2 – {3b + 3c}2
=(2a + 3b + 3c)(2a – 3b – 3c)
Class 9th math bharti bhavan solutions Exercise 3A बहुपद के गुणनखंड pdf solutions
(b) 2x2 − 18y2
हल:
यहाँ,
2x2 − 18y2
=2(x2 – 9y2)
= 2{(x)2 – (3)2}
=2(x + 3)(x – 3)
(c) 50b2c2 − 98a2
हल:
यहाँ,
50b2c2 − 98a2
=2(25b2c2 – 49a2)
= 2{(5bc)2 – (7a)2}
=2(5bc + 7a)(5bc – 7a)
(d) 3x3 − 243xy2
हल:
यहाँ,
3x3 − 243xy2
=3x(x2 – 81y2)
= 3x{(x)2 – (9y)2}
=3x(x + 9y)(x – 9y)
(e) x5 − x3
हल:
यहाँ,
x5 − x3
=x3(x2 – 1)
= x3{(x)2 – (1)2}
=x3(x + 1)(x – 1)
(f) x3 – x
हल:
यहाँ,
x3 – x
=x(x2 – 1)
= x{(x)2 – (1)2}
=x(x + 1)(x – 1)
- गुणनखंड निकाले-
(a)1 − (a2 + b2) + 2ab
हल:
यहाँ,
1 − (a2 + b2) + 2ab
=(1)2 – (a + b)2 – 2ab + 2ab
= (1 + a + b){1 – (a + b)}
= (1 + a + b)(1 – a – b)
(b) b2 + c2 + 2(ab + bc + ca)
हल:
यहाँ,
b2 + c2 + 2(ab + bc + ca)
= (b + c)2 – 2bc + 2ab + 2bc + 2ca
= (b + c)2 + 2ab + 2ca
(c) 25×2 − 10x + 1 − 36y2
(d) x2 − y2 + 6y − 9
- गुणनखंड करे-
4×2 + y2 + z2 − 4xy − 2yz + 4xz
4×2 + 9y2 + 16z2 + 12xy − 24yz − 16xz
x2 + 4y2 + z2 + 4xy − 4yz − 2zx
4×2 + 9y2 + 4z2 − 12xy − 12yz + 8zx
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