Class 8 RD Sharma Solutions – Chapter 7 Factorization – Exercise 7.2

Factorize the following:

Question 1. 3x – 9

Solution:

The highest common factor in the above two terms – 3

3x – 9

3(x – 3)

Question 2. 5x – 15x²

Solution:

The highest common factor in the above two terms – 5x

5x – 15x²

5x (1 – 3x)

Question 3. 20a¹²b² – 15a⁸b⁴

Solution:

The highest common factor in the above two terms – 5a⁸b²

20a¹²b² – 15a⁸b⁴

5a⁸b² (4a⁴ – 3b²)

Question 4. 72x⁶y⁷ – 96x⁷y⁶

Solution:

The highest common factor in the above two terms -24x⁶y⁶

72x⁶y⁷ – 96x⁷y⁶

24x⁶y⁶ (3y – 4x)

Question 5. 20x³ – 40x² + 80x

Solution:

The highest common factor in the above three terms – 20x

20x³ – 40x² + 80x

20x (x² – 2x +4)

Question 6. 2x³y² – 4x²y³ + 8xy⁴

Solution:

The highest common factor in the above three terms – 2xy²

2x³y² – 4x²y³ + 8xy⁴

2xy² (x² – 2xy + 4y²)

Question 7. 10m³n² + 15m⁴n – 20m²n³

Solution:

The highest common factor in the above three terms – 5mn2

10m³n² + 15m⁴n – 20m²n³

5m²n (2mn + 3m² – 4n²)

Question 8. 2a⁴b⁴ – 3a³b⁵ + 4a²b⁵

Solution:

The highest common factor in the above three terms – a²b⁴

2a⁴b⁴ – 3a³b⁵ + 4a²b⁵

a²b⁴ (2a² – 3ab + 4b)

Question 9. 28a² + 14a²b² – 21a⁴

Solution:

The highest common factor in the above three terms – 7a²

28a² + 14a²b² – 21a⁴

7a² (4a + 2b² – 3a²)

Question 10. a⁴b – 3a²b² – 6ab³

Solution:

The highest common factor in the above three terms – ab

a⁴b – 3a²b² – 6ab³

ab (a³ – 3ab – 6b²)

Question 11. 2l²mn – 3lm²n + 4lmn²

Solution:

The highest common factor in the above three terms – lmn

2l²mn – 3lm²n + 4lmn²

lmn (2l – 3m + 4n)

Question 12. x⁴y² – x²y⁴ – x⁴y⁴

Solution:

The highest common factor in the above three terms – x2y2

x⁴y² – x²y⁴ – x⁴y⁴

x²y²(x² – y² – x²y²)

Question 13. 9x²y + 3axy

Solution:

The highest common factor in the above two terms – 3xy

9x²y + 3axy

3xy(3x + a)

Question 14. 16m – 4m²

Solution:

The highest common factor in the above two terms – 4m

16m – 4m²

4m(4 – m)

Question 15. -4a² + 4ab – 4ca

Solution:

The highest common factor in the above three terms – (–4a)

-4a² + 4ab – 4ca

-4a(a – b + c)

Question 16. x²yz + xy²z + xyz²

Solution:

The highest common factor in the above three terms – xyz

x²yz + xy²z + xyz²

xyz(x + y + z)

Question 17. ax²y + bxy² + cxyz

Solution:

The highest common factor in the above three terms – xy

ax²y + bxy² + cxyz

xy(ax + by + cz)