# RBSE Solutions for Class 8 Maths Chapter 10 गुणनखण्ड Ex 10.1

RBSE Solutions for Class 8 Maths Chapter 10 गुणनखण्ड Ex 10.1 is part of RBSE Solutions for Class 8 Maths. Here we have given Rajasthan Board RBSE Class 8 Maths Chapter 10 गुणनखण्ड Exercise 10.1.

 Board RBSE Textbook SIERT, Rajasthan Class Class 8 Subject Maths Chapter Chapter 10 Chapter Name गुणनखण्ड Exercise Exercise 10.1 Number of Questions 3 Category RBSE Solutions

## Rajasthan Board RBSE Class 8 Maths Chapter 10 गुणनखण्ड Ex 10.1

प्रश्न 1
दिए हुए पदों में सार्व गुणनखण्ड(RBSESolutions.com)ज्ञात कीजिए
(i) 12x, 36
(ii) 14pq, 28p2q2
(iii) 6abc, 24ab2, 12a2b
(iv) 16x3, – 4x2, 32x
(v) 10pq, 20qr, 30rp
(vi) 3x2y3, 10x2y2, 6x2y2z
हल:
(i) 12x, 36
12x = 2 x 2 x 3 x x
36 = 2 x 2 x 3 x 3
∴ सार्व गुणनखण्ड = 2 2 x 3 = 12

(ii) 14pq, 28p2q2
14pq = 2 x 7 x p x q2
28p2q2 = 2 x 2 x 7 x p x p x q x q
∴ सार्व गुणनखण्ड = 2 x 7 x p x q = 14pq

(iii) 6abc, 24ab2, 12a2b
6abc = 2 x 3 x 4 x 6 x c
24ab2 = 2 x 2 x 2 x 3 x a x b x b
12a2b = 2 x 2 x 3 x a x a x b
∴ सार्व गुणनखण्ड = 2 x 3 x a x b = 6ab

(iv) 16x3, – 4x2, 32x
16x3 = 2 x 2 x 2 x 2 x x x x x x
– 4x2 = (-1) x 2 x 2 x x x x
32x = 2 x 2 x 2 x 2 x 2 x x
∴ सार्व गुणनखण्ड = 2 x 2 x x = 4x

(v) 10pq, 20qr, 30rp
10pg = 2 x 5 x p x q
20qr = 2 x 2 x 5 x q x r
30rp = 2 x 3 x 5 x r x p
∴ सार्व(RBSESolutions.com)गुणनखण्ड = 2 x 5 = 10

(vi) 3x2y3), 10x2y2, 6x2y2z
3x2y2 = 3 x x x x x y x y x y
10 x2y2 = 2 x 5 x x x x x y x y
6x2y2z = 2 x 3 x x x x x y x y z
∴ सार्व गुणनखण्ड = x x x x y x y = x2y2

प्रश्न 2
निम्नलिखित व्यंजकों के गुणनखण्ड(RBSESolutions.com)कीजिए (सार्वं गुणनखण्ड द्वारा)
(i) 6p – 12
(ii) 7a2 + 14a
(iii) 10a2 – 15b2 + 20c2
(iv) ax2y + bxy2 + cxyz.
(v) x2yz + xy2z + xyz2
(vi) – 16z +20z2
हल:
(i) 6p – 12q
6p – 12q = 6 (p – 2q)

(ii) 7a2 + 14a
7a2+ 14a = 7a (a + 2)

(iii) 10a2 – 15b2 + 20c2
10a2 – 15b2+ 20c2
= 5 (2a2 – 3b2+ 4c2)

(iv) ax2y + bxy2 + cxyz
ax2y + bxy2+ cxyz
= xy (ax + by + cz)

(v) x2yz + xy2z + xyz2
x2yz + xy2z + xyz2
= xyz (x + y + z)

(vi) – 16z + 20z3
– 16z + 20z3
= 4z (-4 + 5z2)

प्रश्न 3
गुणनखण्ड कीजिए(RBSESolutions.com)(समूहन द्वारा)
(i) 2xy + 3 + 2y + 3x
(ii) z – 7 – 7xy + xyz
(iii) 6ry – 4y + 6 – 9
(iv) 15pq + 15 + 99 + 25p
हल:
(i) 2xy + 3 + 2y + 3x
2xy + 3 + 2y + 3x
= 2xy + 2y + 3 + 3x
= 2y (x + 1) + 3(1 + x)
= 2y (x + 1) + 3 (x + 1)
= (x + 1) (2y + 3)

(ii) z – 7 – 7xy + xyz
z – 77xy + xyz
= z – 7 – xy (7 – z)
= 1 (z – 7) + xy (z – 7)
= (1 + xy) (z – 7)
= (xy + 1) (z – 7)

(iii) 6xy – 4y + 6 – 9x
6xy – 4y + 6 – 9x
= 2y (3x – 2) + 3(2 – 3x)
= 2y (3x – 2) – 3(3x – 2)
= (3x – 2) (2y – 3)

(iv) 15pq + 15 +9q + 25p
15pq + 15 + 9q + 25p
= 15pq + 9q + 15 + 25p
= 3q (5p + 3) + 5(3 + 5p)
= 3q (5p + 3) + 5 (5p + 3)
= (5p + 3) (3q + 5)

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