**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 – 15x**^{2}

^{2}

**Solution:**

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

5x – 15x

^{2}5x (1 – 3x)

**Question 3. 20a**^{12}b^{2} – 15a^{8}b^{4}

^{12}b

^{2}– 15a

^{8}b

^{4}

**Solution:**

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

^{8}b^{2}20a

^{12}b^{2}– 15a^{8}b^{4}5a

^{8}b^{2}(4a^{4}– 3b^{2})

**Question 4. 72x**^{6}y^{7} – 96x^{7}y^{6}

^{6}y

^{7}– 96x

^{7}y

^{6}

**Solution:**

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

^{6}y^{6}72x

^{6}y^{7}– 96x^{7}y^{6}24x

^{6}y^{6}(3y – 4x)

**Question 5. 20x**^{3} – 40x^{2} + 80x

^{3}– 40x

^{2}+ 80x

**Solution:**

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

20x

^{3}– 40x^{2}+ 80x20x (x

^{2}– 2x +4)

**Question 6. 2x**^{3}y^{2} – 4x^{2}y^{3} + 8xy^{4}

^{3}y

^{2}– 4x

^{2}y

^{3}+ 8xy

^{4}

**Solution:**

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

^{2}2x

^{3}y^{2}– 4x^{2}y^{3}+ 8xy^{4}2xy

^{2}(x^{2}– 2xy + 4y^{2})

**Question 7. 10m**^{3}n^{2} + 15m^{4}n – 20m^{2}n^{3}

^{3}n

^{2}+ 15m

^{4}n – 20m

^{2}n

^{3}

**Solution:**

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

10m

^{3}n^{2}+ 15m^{4}n – 20m^{2}n^{3}5m

^{2}n (2mn + 3m^{2}– 4n^{2})

**Question 8. 2a**^{4}b^{4} – 3a^{3}b^{5} + 4a^{2}b^{5}

^{4}b

^{4}– 3a

^{3}b

^{5}+ 4a

^{2}b

^{5}

**Solution:**

The highest common factor in the above three terms – a

^{2}b^{4}2a

^{4}b^{4}– 3a^{3}b^{5}+ 4a^{2}b^{5}a

^{2}b^{4}(2a^{2}– 3ab + 4b)

**Question 9. 28a**^{2} + 14a^{2}b^{2} – 21a^{4}

^{2}+ 14a

^{2}b

^{2}– 21a

^{4}

**Solution:**

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

^{2}28a

^{2}+ 14a^{2}b^{2}– 21a^{4}7a

^{2}(4a + 2b^{2}– 3a^{2})

**Question 10. a**^{4}b – 3a^{2}b^{2} – 6ab^{3}

^{4}b – 3a

^{2}b

^{2}– 6ab

^{3}

**Solution:**

The highest common factor in the above three terms – ab

a

^{4}b – 3a^{2}b^{2}– 6ab^{3}ab (a

^{3}– 3ab – 6b^{2})

**Question 11. 2l**^{2}mn – 3lm^{2}n + 4lmn^{2}

^{2}mn – 3lm

^{2}n + 4lmn

^{2}

**Solution:**

The highest common factor in the above three terms – lmn

2l

^{2}mn – 3lm^{2}n + 4lmn^{2}lmn (2l – 3m + 4n)

**Question 12. x**^{4}y^{2} – x^{2}y^{4} – x^{4}y^{4}

^{4}y

^{2}– x

^{2}y

^{4}– x

^{4}y

^{4}

**Solution:**

The highest common factor in the above three terms – x2y2

x

^{4}y^{2}– x^{2}y^{4}– x^{4}y^{4}x

^{2}y^{2}(x^{2}– y^{2}– x^{2}y^{2})

**Question 13. 9x**^{2}y + 3axy

^{2}y + 3axy

**Solution:**

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

9x

^{2}y + 3axy3xy(3x + a)

**Question 14. 16m – 4m**^{2}

^{2}

**Solution:**

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

16m – 4m

^{2}4m(4 – m)

**Question 15. -4a**^{2} + 4ab – 4ca

^{2}+ 4ab – 4ca

**Solution:**

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

-4a

^{2}+ 4ab – 4ca-4a(a – b + c)

**Question 16. x**^{2}yz + xy^{2}z + xyz^{2}

^{2}yz + xy

^{2}z + xyz

^{2}

**Solution:**

The highest common factor in the above three terms – xyz

x

^{2}yz + xy^{2}z + xyz^{2}xyz(x + y + z)

**Question 17. ax**^{2}y + bxy^{2} + cxyz

^{2}y + bxy

^{2}+ cxyz

**Solution:**

The highest common factor in the above three terms – xy

ax

^{2}y + bxy^{2}+ cxyzxy(ax + by + cz)