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 – 7 – 7xy + 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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