Class 8 RD Sharma Solutions Chapter 7 Factorization  Exercise 7.1 (original) (raw)

Last Updated : 11 Sep, 2024

**Question 1. **Find (GCF/HCF) of 2x 2 and 12x 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

2x2 = 2 * x * x

12x2 = 2* 2 * 3 * x * x

**GCF(2x 2 , 12x 2 ) = 2 * x * x

**= 2x 2

**Question 2. Find (GCF/HCF) of 6x 3 y and 18x 2 y 3

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

6x3y = 2 * 3 * x * x * x * y

18x2y3 = 2 * 2 * 3 * x * x * y * y * y

**GCF(6x 3 y, 18x 2 y 3 ) = 2 * 3 * x * x * y

**= 6x 2 y

**Question 3. Find (GCF/HCF) of 7x, 21x 2 and 14xy 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

7x = 7 * x

21x2 = 7 * 3 * x * x

14xy2 = 7 * 2 * x * y * y

**GCF(7x, 21x 2 , 14xy 2 ) = 7*x

= 7x

**Question 4. Find (GCF/HCF) of 42x 2 yz and 63x 3 y 2 z 3

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

42x2yz = 2 * 3 * 7 * x * x * y * z

63x3y2z3 = 3 * 3 * 7 * x * x * x * y * y * z * z * z

**GCF(42x 2 yz, 63x 3 y 2 z 3 ) = 3 * 7 * x * x * y * z

= 21x 2 yz

**Question 5. Find (GCF/HCF) of 12ax 2 , 6a 2 x 3 and 2a 3 x 5

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

12ax2 = 2 * 2 * 3 * a * x * x

6a2x3 = 2 * 3 * a * a * x * x * x

2a3x5 = 2 * a * a * a * x * x * x * x * x

**GCF(12ax 2 , 6a 2 x 3 ,2a 3 x 5 ) = 2 * a * x * x

= 2ax 2

**Question 6. Find (GCF/HCF) of 9x 2 , 15x 2 y 3 , 6xy 2 **and 21x 2 y 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

9x2 = 3 * 3 * x * x

15x2y3 = 3 * 5 * x * x * y * y * y

6xy2 = 2 * 3 * x * y * y

21x2y2 = 3 * 7 * x * x * y * y

**GCF(9x 2 , 15x2y 3 , 6xy 2 **and 21x 2 y 2 ) = 3 * x

= 3x

**Question 7. Find (GCF/HCF) of 4a 2 b 3 , -12a 3 b, 18a 4 b 3

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

4a2b3 = 2 * 2 * a * a * b * b * b

-12a3b = -1 * 2 * a * a * a * b

18a4b3 = 2 * 3 * 3 * a * a * a * a * b * b * b

**GCF(4a 2 b 3 , -12a 3 b, 18a 4 b 3 ) = 2 * a * a * b

= 2a 2 b

**Question 8. Find (GCF/HCF) of 6x 2 y 2 , 9xy 3 , 3x 3 y 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

6x2y2 = 2 * 3 * x * x * y * y

9xy3 = 3 * x * y * y * y

3x3y2 = 3 * x * x * x * y * y

**GCF(6x 2 y 2 , 9xy 3 , 3x 3 y 2 ) = 3 * x * y * y

= 3xy 2

**Question 9. Find (GCF/HCF) of a 2 b 3 , a 3 b 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

a2b3 = a * a * b * b * b

a3b2 = a * a * a * b * b

**GCF(a 2 b 3 , a 3 b 2 ) = a * a * b * b

= a 2 b 2

**Question 10. Find (GCF/HCF) of 36a 2 b 2 c 4 , 54a 5 c 2 , 90a 4 b 2 c 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

36a2b2c4 = 2 * 2 * 3 * 3 * a * a * b * b * c * c * c * c

54a5c2 = 2 * 3 * 3 * 3 * a * a * a * a * a * c * c

90a4b2c2 = 2 * 3 * 3 * 5 * a * a * a * a * b * b * c * c

**GCF(36a 2 b 2 c 4 , 54a 5 c 2 , 90a 4 b 2 c 2 ) = 2 * 3 * 3 * a * a * c * c

= 18a 2 c 2

**Question 11. Find (GCF/HCF) of x 3 , -yx 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

x3 = x * x * x

-yx2 = -1 * y * x * x

**GCF(x 3 , -yx 2 ) = x * x

= x 2

**Question 12. Find (GCF/HCF) of 15a 3 , -45a 2 , -150a

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

15a3 = 3 * 5 * a * a * a

-45a2 = -1 * 3 * 3 * 5 * a *a

-150a = -1 * 2 * 3 * 5 * 5 * a

**GCF(15a 3 , -45a 2 , -150a) = 3 * 5 * a

= 15a

**Question 13. Find (GCF/HCF) of 2x 3 y 2 , 10x 2 y 3 , 14xy

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

2x3y2 = 2 * x * x * x * y * y

10x2y3 = 2 * 5 * x * x * y * y * y

14xy = 2 * 7 * x * y

**GCF(2x 3 y 2 , 10x 2 y 3 , 14xy) = 2 * x * y

= 2xy

**Question 14. Find (GCF/HCF) of 14x 3 y 5 , 10x 5 y 3 , 2x 2 y 2

**Solution:

First Prime Factorize each monomial, then find common among them.

Here,

14x3y5 = 2 * 7 * x * x * x * y * y * y * y * y

10x5y3 = 2 * 5 * x * x * x * x * x * y * y * y

2x2y2 = 2 * x * x * y * y

**GCF(14x 3 y 5 , 10x 5 y 3 , 2x 2 y 2 ) = 2 * x * x * y * y

= 2x 2 y 2

**Find the greatest common factor(GCF) of the terms in the following expressions. (Q15 - Q17)

**Question 15. 5a 4 **+ 10a 3 **- 15a 2

**Solution:

Here, 5a4 = 5 * a * a * a * a

10a3 = 2 * 5 * a * a * a

-15a2 = -1 * 3 * 5 * a * a

5a4 + 10a3 - 15a2 = (5 * a * a * a * a) + (2 * 5 * a * a * a) + (-1 * 3 * 5 * a * a)

= 5a2(a2 + 2a - 3)

**GCF(5a 4 **+ 10a 3 **- 15a 2 ) = 5a 2

**Question 16. 2xyz + 3x 2 y + 4y 2

**Solution:

Here, 2xyz = 2 * x * y * z

3x2y = 3 * x * x * y

4y2 = 2 * 2 * y * y

2xyz + 3x2y + 4y2 = (2 * x * y * z) + (3 * x * x * y) + (4 * y * y)

= y(2x + 3x2 + 4y)

**GCF(2xyz + 3x 2 y + 4y 2 ) = y

**Question 17. 3a 2 b 2 **+ 4b 2 c 2 **+ 12a 2 b 2 c 2

**Solution:

Here, 3a2b2 = 3 * a * a * b * b

4b2c2 = 2 * 2 * b * b * c * c

12a2b2c2 = 2 * 2 * 3 * a * a * b * b * c * c

3a2b2 + 4b2c2 + 12a2b2c2 = (3 * a * a * b * b) + (2 * 2 * b * b * c * c) + (2 * 2 * 3 * a * a * b * b * c * c)

= b(3a2b + 4bc2 + 12a2bc2)

**GCF(3a 2 b 2 **+ 4b 2 c 2 **+ 12a 2 b 2 c 2 ) = b

Summary

Exercise 7.1 in the RD Sharma Class 8 textbook is designed to help students develop a strong foundation in factorizing linear expressions. The practice questions cover a wide range of scenarios, including expressions with a single variable, expressions with multiple variables, and expressions involving common factors. By working through these questions, students will learn to identify the appropriate factorization techniques, apply them correctly, and simplify the given expressions. Mastering the skills covered in this exercise will enable students to tackle more complex algebraic problems and lay the groundwork for further exploration of factorization concepts.