Haryana Board Class 8 Maths Algebra Chapter 14 Factorisation

Factorisation Of Algebraic Expressions

Question 1. Resolve into factors:

1. x² – 22x + 120

Solution:

Given: x² – 22x + 120

= x²-10x-12x-120

= x(x-10)-12(x-10)

= (x-10) (x-12)

x² – 22x + 120 = (x-10) (x-12)

2. 40+3x-x²

Solution:

Given: 40+3x-x²

= 40+8x-5x-x²

= 8(5+x)-x(5+x)

= (8-x)(5+x)

40+3x-x² = (8-x)(5+x)

Haryana Board Class 8 Maths Factorisation Solutions

3. (a²-a)²-8(a²-a)+12

Solution:

Given: (a²-a)²-8(a²-a)+12

= (a²-a)² – 6(a²-a)-2(a²-a)+12

= (a²−a)((a²-a)−6)-2((a²-a)-6)

= (a²-a-2) (a²-a-6)

= (a²+a-2a-2)(a²3a+2a-6)

= (a(a+1)-2(a+1))(a(a-3)+2(9-3))

= (a+1) (a-2) (a+2) (a-3)

(a²-a)²-8(a²-a)+12 = (a+1) (a-2) (a+2) (a-3)

4. x²-√3x-6

Solution:

Given: x²-√3x-6

= x²-2√3x+√3x-6

= x(x-2√3)+ √3(x-2√3)

= (x+√3)(x-2√3)

x²-√3x-6 = (x+√3)(x-2√3)

Class 8 Maths Chapter 14 Factorisation Haryana Board

5. (x+1)(x+3)(x-4)(x-6)+13

Solution:

Given (x+1)(x+3)(x-4)(x-6)+ 13

= (x²+3x+x+3)(x²-6x-4x+24)+13

= (x²+4x+3)(x²-10x+24)+13

= x⁴-10x³+24x²+4x³40x²+96x+3x² = 30x+72+13

= x⁴-6x³-13x²-66+85

= x⁴-3x³-3x³-17x²+9x²– 5x²+51x+15x+85

= x⁴-3x³-17x²-3x³+9x²+51x-5x²+15x+85

= x²(x²-3x-17)-3x(x²-3x-17)-5(x²-3x-17)

= (x²-3x-5)(x²-3x-17)

(x+1)(x+3)(x-4)(x-6)+ 13 = (x²-3x-5)(x²-3x-17)

6. 21x² + 40xy – 21y²

Solution:

Given: 21x²+40xy-21y²

= 21x² – 9xy + 49xy – 21y²

= 3x(7x-3y) + 7y(7x-3y)

= (3x+7y)(7x-3y)

21x²+40xy-21y² = (3x+7y)(7x-3y)

Haryana Board 8th Class Maths Factorisation Questions and Answers

7. 4(2a-3)² -3(2a-3) (a-1)-7(a-1)²

Solution:

Given: 4(2a-3)²-3(2a-3) (a-1)-7(a-1)²

= 4(4a²-(2a+9)-3(2a²-2a-3a+3)-7(a²+1-2a)

= 16a² – 48a + 36 – 6a² + 6a + 9a – 9 – 7a² – 7 + 14

= 3a² – 19a + 20

= 3a² – 15a – 4a +20

= 3(a-5)-4(a-5)

4(2a-3)²-3(2a-3) (a-1)-7(a-1)² = (3a-4) (a-5)

8. (a+7) (a-10) + 16

Solution:

Given: (a+7)(a-10)+16

= a²-10a+7a-70+16

= a²-3a-54

= a-9a+6a-54

= a(a-9)+6(a-9)

=(a+6)(a-9)

(a+7)(a-10)+16 =(a+6)(a-9)

Chapter 14 Factorisation Class 8 Solutions in Hindi Haryana Board

9. (a²+4a)²+21(a²+4a)+98

Solution:

Given: (a²+4a)²+21(a²+4a)+98

= a⁴ + 8a³ + 16a² + 2(a²+4a)+ 98

= a⁴ + 8a³ + 37a² +84a +98

= a⁴+4a³+14a²+4a³+16a²+56a+7a²+28+98

= a² (a²+4a+14)+4a(a²+4a+14) +7(a²+4a+14)

= (a²+4a+7) (a² + 4a + 14)

(a²+4a)²+21(a²+4a)+98 = (a²+4a+7) (a² + 4a + 14)

10. (2a²+ 5a) (2a² + 5a-19) +84

Solution:

Given: (2a²+ 5a) (2a² + 5a-19) +84

= 4a⁴ + 10a³ – 38a² + 10a³ + 25a² – 95a + 84

= 4a⁴ + 20a³ – 13a² – 95a + 84

= 4a⁴ + 8a³ – 21a² + 12a³ + 24a² – 63a -16a² – 32a + 84

= a²(4a²+8a-21)+3a(4a²+8a-21)-4(4a²+8a-21)

= (a²+3a-4) (4a² +8a-21)

= (a²+4a-a-4) (4a² + 14a-6a-21)

= ((a+4)a-1(a+4)) (2a(2a+7)-3(2a+7))

= (a-1) (a+4) (2a-3)(2a+7)

(2a²+ 5a) (2a² + 5a-19) +84 = (a-1) (a+4) (2a-3)(2a+7)

11. 8x⁴+2x²-45

Solution:

Given: 8x⁴+2x²-45

= 8x² + 20x² – 18x² – 45

= 4x² (2x²+5)-9(2x²+5)

= (2x²+5)(4x²-9)

= (2x+5) (4x²-6x+6x-9)

= (2x²+5) (2x(2x-3)+3(2x-3))

= (2x²+5)(2x+3)(2x-3)

8x⁴+2x²-45 = (2x²+5)(2x+3)(2x-3)

Haryana Board Class 8 Maths Exercise 14.1 Solutions

12. xv-x-(a-3)(a-2)

Solution:

Given: x²-x-(a-3)(a-2)

= x²-x-(a²-2a-3a+6)

= x²-x-a²+5a-6

= x²-3x+2x-a²+ax-ax+3a+2a-6

= x²+ax-3x-ax-a²+3a+2x+2a-6

= x(x+a-3)-a(x+a-3)+2(x+a-3)

=(x-a+2)(x+a-3)

x²-x-(a-3)(a-2) =(x-a+2)(x+a-3)

13. 99x²-20xy+99y²

Solution:

Given: 99x²-20xy+99y²

= 99x²-81xy-121xy+99y²

= 9x (11x-9y)-11y (11x-94)

= (9x-114) (11x-94)

99x²-20xy+99y²  = (9x-114) (11x-94)

Question 2. Resolve the following expressions into factors by expressing them as the diffence of two Squares:

1. x²-5x-6

Solution:

Given: x²-5x-6

= x²-6x+x-6

= x(x-6)+1(x-6)

= (x+1)(x-6)

x²-5x-6 = (x+1)(x-6)

2. 3+x-10x²

Solution:

Given: 3+x-10x²

= 3+6x-5x-10x²

= 3(1+2x)-5x(1+2x)

= (3-5x) (1+2x)

3+x-10x² = (3-5x) (1+2x)

3. 8x-3-4x²

Solution:

Given: 8x-3-4x²

= 6x+2x-3-4x²

= 6x-3+2x-4x²

= 3(2x-1)-2x(2x-1)

= (3-2x) (2x-1)

8x-3-4x²= (3-2x) (2x-1)

4. 6(a+b)²+5(a²-b²)-6 (a-b)²

Solution:

Given: 6(a+b)²+5(a²-b²)-6(a-b)²

= 6(a²+b²+2ab)+5a²-5b²-6(a²+b²-2ab)

= 6a²+6b²+ 12ab+ 5a²-5b²-6a²-6b² +12ab

= 5a²+24ab-5b²

= 5a² +25ab-ab-5b²

= 5a(a+5b)-b(a+5b)

= (5a-b)(a+5b)

6(a+b)²+5(a²-b²)-6(a-b)² = (5a-b)(a+5b)

5. 6x²-13x+6

Solution:

Given: 6x²-13x+6

= 6x²-9x-4x+6

= 3x(2x-3)-2(2x-3)

=(3x-2)(2x-3)

6x²-13x+6 =(3x-2)(2x-3)

Question 3. Choose the Correct answer:

1. x²-3x-28 = ?

1. (x+4)(x+7)
2. (x+4)(x-7)
3. (x-4)(x+7)
4. (x-4)(x-7)

Solution:

x²-3x-28

= x²-7x+4x-28

= x(x-7)+4(x-7)

= (x+4) (x-7)

x²-3x-28 = (x+4) (x-7)

The Correct answer is (2)

Important Questions for Class 8 Maths Chapter 14 Haryana Board

2) If (5x²-4x-9) = (x+1)(5x+P), then the value of P is

1. 9
2. 5
3. -9
4. none of these

Solution:

= 5x²-4x-9

= 5x²-9x+5x-9 = x(5x-9)+1(5x-9)

= (5x-9)(x+1)

= (x+1)(5x+P)= (x+1) (5x-9)

= 5x + P = 5x-9

⇒ P = -9

The value of P = -9

The Correct answer is (3).

3. 2a²+b²-c²+3ab+ac = ?

1. (a+b+c)(2a+b+c)
2. (a+b+c)(2a+b-c)
3. (a+b+c) (2a-b-c)
4. none of these

Solution:

2a²+b²-c²+3ab+ac

= 2a²+ab-ac+2ab+b²-bc+2ac + bc-c²

= a(2a+b-c)+b(2a+b-c) + C(2a+b-c)

= (a+b+c) (2a+b-c)

2a²+b²-c²+3ab+ac = (a+b+c) (2a+b-c)

The Correct answer is (2).

Question 4. write ‘True’ or ‘False’:

1. The Factors of (x²-xy-30y²) is (x+5y)(x-64).

Solution:

x²-xy-30y² = x²-6xy+5xy-30y²

= x(x-6y) +5y(x-6y) = (x-6y) (x+5y)

The statement is true.

Step-by-Step Solutions for Factorisation Class 8 Haryana Board

2. a³-b³-a(a²-b²)+b(a-b)²=ab(a-b)

Solution:

a³-b³-a(a²-b²)+b(a-b)²=ab(a-b)

= a³-b³-a³+ab²+b(a²+b²-2ab)

= -b³+ab²+ba²+b³-2ab²

= a²b-ab² = ab(a-b)

The statement is true.

3.(x-1)(x+9)+21=(x+6)(x-2)

Solution:

(x-1)(x+9)+21

= x²+9x-x-9+21

= x²+8x+12

= x²+6x+2x+12

= x(x+6)+2(x+6)

= (x+2)(x+6)

The statement is false.

Question 5. Fill in the blanks:

1. (x+a)(x+b) = x²+(a+b)x + _______.

Solution:

(x+9)(x+6) = x(x+b)+a(x+b)

= x²+bx+ax+ab = x²+(a+b)x+ab

2. (a+b+c)³ = a³ + b² + c² + __________.

Solution:

3(a+b)(b+c)(c+a).