### Chapter 7 Factorization – Exercise 7.8 | Set 1

**Question 11. 12x**^{2} – 17xy + 6y^{2}

^{2}– 17xy + 6y

^{2}

**Solution:**

Given:12x

^{2}– 17xy + 6y^{2}The coefficient of x

^{2}= 12The coefficient of x = -17y

Constant term = 6y

^{2}So, we write the middle term -17xy as -9xy – 8xy

12x

^{2}-17xy+ 6y^{2}= 12x^{2}– 9xy – 8xy + 6y^{2}= 3x (4x – 3y) – 2y (4x – 3y)

= (3x – 2y) (4x – 3y)

**Question 12. 6x**^{2} – 5xy – 6y^{2}

^{2}– 5xy – 6y

^{2}

**Solution:**

Given:6x

^{2}– 5xy – 6y^{2}The coefficient of x

^{2}= 6The coefficient of x = -5y

Constant term = -6y2

So, we write the middle term -5xy as 4xy – 9xy

6x

^{2}-5xy- 6y^{2}= 6x^{2}+ 4xy – 9xy – 6y^{2}= 2x (3x + 2y) -3y (3x + 2y)

= (2x – 3y) (3x + 2y)

**Question 13. 6x**^{2} – 13xy + 2y^{2}

^{2}– 13xy + 2y

^{2}

**Solution:**

Given:6x

^{2}– 13xy + 2y^{2}The coefficient of x

^{2}= 6The coefficient of x = -13y

Constant term = 2y

^{2}So, we write the middle term -13xy as -12xy – xy

6x

^{2}-13xy+ 2y^{2}= 6x^{2}– 12xy – xy + 2y^{2}= 6x (x – 2y) – y (x – 2y)

= (6x – y) (x – 2y)

**Question 14. 14x**^{2} + 11xy – 15y^{2}

^{2}+ 11xy – 15y

^{2}

**Solution:**

Given:14x

^{2}+ 11xy – 15y^{2}The coefficient of x

^{2}= 14The coefficient of x = 11y

Constant term = -15y

^{2}So, we write the middle term 11xy as 21xy – 10xy

14x

^{2}+ 11xy- 15y^{2}= 14x^{2}+ 21xy – 10xy – 15y^{2}= 2x (7x – 5y) + 3y (7x – 5y)

= (2x + 3y) (7x – 5y)

**Question 15. 6a**^{2} + 17ab – 3b^{2}

^{2}+ 17ab – 3b

^{2}

**Solution:**

Given:6a

^{2}+ 17ab – 3b2The coefficient of a

^{2}= 6The coefficient of a = 17b

Constant term = -3b

^{2}So, we write the middle term 17ab as 18ab – ab

6a

^{2}+17ab– 3b^{2}= 6a^{2}+ 18ab – ab – 3b^{2}= 6a (a + 3b) – b (a + 3b)

= (6a – b) (a + 3b)

**Question 16. 36a**^{2} + 12abc – 15b^{2}c^{2}

^{2}+ 12abc – 15b

^{2}c

^{2}

**Solution:**

Given:36a

^{2}+ 12abc – 15b^{2}c^{2}The coefficient of a

^{2}is 36The coefficient of a is 12bc

Constant term is -15b

^{2}c^{2}So, we write the middle term 12abc as 30abc – 18abc

36a

^{2}–12abc– 15b^{2}c^{2}= 36a^{2}+ 30abc – 18abc – 15b^{2}c^{2}= 6a (6a + 5bc) – 3bc (6a + 5bc)

= (6a + 5bc) (6a – 3bc)

= (6a + 5bc) 3(2a – bc)

**Question 17. 15x**^{2} – 16xyz – 15y^{2}z^{2}

^{2}– 16xyz – 15y

^{2}z

^{2}

**Solution:**

Given:15x

^{2}– 16xyz – 15y^{2}z^{2}The coefficient of x

^{2}= 15The coefficient of x = -16yz

Constant term = -15y

^{2}z^{2}So, we write the middle term -16xyz as -25xyz + 9xyz

15x

^{2}-16xyz- 15y^{2}z^{2}= 15x^{2}– 25yz + 9yz – 15y^{2}z^{2}= 5x (3x – 5yz) + 3yz (3x – 5yz)

= (5x + 3yz) (3x – 5yz)

**Question 18. (x – 2y)**^{2} – 5 (x – 2y) + 6

^{2}– 5 (x – 2y) + 6

**Solution:**

Given:(x – 2y)

^{2}– 5 (x – 2y) + 6The coefficient of (x-2y)

^{2}= 1The coefficient of (x-2y) = -5

Constant term = 6

So, we write the middle term -5(x – 2y) as -2(x – 2y) -3(x – 2y)

(x – 2y)

^{2}– 5 (x – 2y) + 6 = (x – 2y)^{2}– 2 (x – 2y) – 3 (x – 2y) + 6= (x – 2y – 2) (x – 2y – 3)

**Question 19. (2a – b)**^{2} + 2 (2a – b) – 8

^{2}+ 2 (2a – b) – 8

**Solution:**

Given:(2a – b)

^{2}+ 2 (2a – b) – 8The coefficient of (2a-b)

^{2}= 1The coefficient of (2a-b) = 2

Constant term = -8

So, we write the middle term 2(2a – b) as 4 (2a –b) – 2 (2a – b)

(2a – b)

^{2}+ 2 (2a – b) – 8 = (2a – b)^{2}+ 4 (2a – b) – 2 (2a – b) – 8= (2a – b) (2a – b + 4) – 2 (2a – b + 4)

= (2a – b + 4) (2a – b – 2)