RS Aggarwal Class 8 Math Seventh Chapter Factorisation Exercise 7D Solution

RS Aggarwal Class 8 Math Seventh Chapter Factorisation Exercise 7D Solution

EXERCISE 7D

Factorise:

(1) x² + 5x + 6

Solution: Find two numbers whose sum = (2 + 3) = 5 and product = (2 × 3) = 6

∴ x² + 5x + 6

= x² + (3+2)x + 6

= x² + 3x + 2x + 6

= x (x + 3) + 2(x + 3)

= (x+ 3) (x + 2)

(2) y² + 10y + 24

= y² + (6 + 4)y + 24

= y² + 6y + 4y + 24

= y(y + 6) + 4(y + 6)

= (y+ 6) (y + 4)

(3) z² + 12z + 27

= z² + (9 + 3)z + 27

= z² + 9z + 3z + 27

= z (z + 9) + 3(z + 9)

= (z + 9) (z + 3)

(4) p² + 6p + 8

= p² + (4 + 2)p + 8

= p² + 4p + 2p + 8

= p (p + 4) + 2 (p + 4)

= (p + 4) (p + 2)

(5) x² + 15x + 56

= x² + (8 + 7)x + 56

= x² + 8x + 7x + 56

= x(x + 8) + 7(x + 8)

= (x + 8) (x + 7)

(6) y² + 19y + 60

= y² + (15 + 4)y + 60

= y² + 15y + 4y + 60

= y(y + 15) + 4(y + 15)

= (y + 15) (y + 4)

(7) x² + 13x + 40

= x² + (5 + 8) x + 40

= x² + 5x + 8x+ 40

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

= (x + 5) (x + 8)

(8) q² – 10q + 21

= q² – (7 + 3)q + 21

= q² – 7q – 3q + 21

= q (q – 7) – 3 (q – 7)

= (q – 7) (q – 3)

(9) p² + 6p – 16

Solution: Find two numbers whose difference is 6 and product 16.

= p² + (8 – 2)p – 16

= p² + 8p – 2p – 16

= p (p + 8) – 2 (p + 8)

= (p + 8) (p – 2)

(10) x² – 10x + 24

= x² – (6 + 4)x + 24

= x² – 6x – 4x + 24

= x (x – 6) – 4 (x – 6)

= (x – 6) (x – 4)

(11) x² – 23x + 42

= x² – (21 + 2)x + 42

= x² – 21x – 2x + 42

= x (x – 21) – 2(x – 21)

= (x – 21) (x – 2)

(12) x² – 17x + 16

= x² – (16 + 1)x + 16

= x² – 16x – 1x + 16

= x (x – 16) – 1(x – 16)

= (x – 16) (x – 1)

(13) y² – 21y + 90

= y² – (15 + 6)y + 90

= y² – 15y – 6y + 90

= y (y – 15) – 6(y – 15)

= (y – 15) (y – 6)

(14) x² – 22x + 117

= x² – (13 + 9)x + 117

= x² – 13x – 9x + 177

= x (x – 13) – 9(x – 13)

= (x – 13) (x – 9)

(15) x² – 9x + 20

= x² – (4 + 5)x + 20

= x² – 4x – 5x + 20

= x (x – 4) – 5 (x – 4)

= (x – 4) (x – 5)

(16) x² + x – 132

= x² + (12 – 11)x – 132

= x² + 12x – 11x – 132

= x (x + 12) – 11(x + 12)

= (x + 12) (x – 11)

(17) x² + 5x – 104

= x² + (13 – 8)x – 104

= x² + 13x – 8x – 104

= x (x + 13) – 8(x + 13)

= (x + 13) (x – 8)

(18) y² + 7y – 144

= y² + (16 – 9)y – 144

= y² + 16y – 9y – 144

= y (y + 16) – 9(y + 16)

= (y + 16) (y – 9)

(19) z² + 19z – 150

= z² + (25 – 6)z – 150

= z² + 25z – 6z – 150

= z (z + 25) – 6(z + 25)

= (z + 25) (z – 6)

(20) y² + y – 72

= y² + (9 – 8)y – 72

= y² + 9y – 8y – 72

= y (y + 9) – 8(y + 9)

= (y + 9) (y – 8)

(21) a² + 6a – 91

= a² + (13 – 7)a – 91

= a² + 13a – 7a – 91

= a(a + 13) – 7(a + 13)

= (a + 13) (a – 7)

(22) p² – 4p – 77

= p² – (11 – 7)p – 77

= p² – 11p + 7p – 77

= p(p – 11) + 7(p – 11)

= (p – 11) (p + 7)

(23) x² – 7x – 30

= x² – (10 – 3)x – 30

= x² – 10x + 3x – 30

= x (x – 10) + 3(x – 10)

= (x – 10) (x + 3)

(24) x² – 11x – 42

= x² – (14 – 3)x – 42

= x² – 14x + 3x – 42

= x(x – 14) + 3(x – 14)

= (x – 14) (x + 3)

(25) x² – 5x – 24

= x² – (8 – 3)x – 24

= x² – 8x + 3x – 24

= x(x – 8) + 3(x – 8)

= (x – 8) (x + 3)

(26) y² – 6y – 135

= y² – 6y – 135

= y² – (15 – 9)y – 135

= y² – 15y + 9y – 135

= y (y – 15) + 9(y – 15)

= (y – 15) (y + 9)

(27) z² – 12z – 45

= z² – (15 – 3)z – 45

= z² – 15z + 3z – 45

= z(z – 15) + 3(z – 15)

= (z – 15) (z + 3)

(28) x² – 4x – 12

= x² – (6 – 2)x – 12

= x² – 6x + 2x – 12

= x (x – 6) + 2(x – 6)

= (x – 6) (x + 2)

(29) 3x² + 10x + 8

= 3x² + (6 + 4)x + 8

= 3x² + 6x + 4x + 8

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

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

(30) 3y² + 14y + 8

= 3y² + (12 + 2)y + 8

= 3y² + 12y + 2y + 8

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

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

(31) 3z² – 10z + 8

= 3z² – (6 + 4) z + 8

= 3z² – 6z – 4z + 8

= 3z (z – 2) – 4 (z – 2)

= (z – 2) (3z – 4)

(32) 2x² + x – 45

= 2x² + (10 – 9)x – 45

= 2x² + 10x – 9x – 45

= 2x(x + 5) – 9(x + 5)

= (x + 5) (2x – 9)

(33) 6p² + 11p – 10

= 6p² + (15 – 4)p – 10

= 6p² + 15p – 4p – 10

= 3p (2p + 5) – 2(2p + 5)

= (2p + 5) (3p – 2)

(34) 2x² – 17x – 30

= 2x² – (20 – 3)x – 30

= 2x² – 20x + 3x – 30

= 2x (x – 10) + 3(x – 10)

= (x – 10) (2x + 3)

(35) 7y² – 19y – 6

= 7y² – (21 – 2)y – 6

= 7y² – 21y + 2y – 6

= 7y (y – 3) + 2 (y – 3)

= (7y + 2) (y – 3)

(36) 28 – 31x – 5x²

= 28 – (35 – 4)x – 5x²

= 28 – 35x + 4x – 5x²

= 7(4 – 5x) + x (4 – 5x)

= (4 – 5x) (7 + x)

(37) 3 + 23z – 8z²

= 3 + (24 – 1)z – 8z²

= 3 + 24z – 1z – 8z²

= 3 (1 + 8z) – z(1 + 8z)

= (1 + 8z) (3 – z)

(38) 6x² – 5x – 6

= 6x² – (9 – 4)x – 6

= 6x² – 9x + 4x – 6

= 3x (2x – 3) + 2(2x – 3)

= (2x – 3) (3x + 2)

(39) 3m² + 24m + 36

= 3m² + (18 + 6)m + 36

= 3m² + 18m + 6m + 36

= 3m (m + 6) + 6(m + 6)

= (m + 6) (3m + 6)

(40) 4n² – 8n + 3

= 4n² – (6 + 2)n + 3

= 4n² – 6n – 2n + 3

= 2n(2n – 3) – 1(2n – 3)

= (2n – 3) (2n – 1)

(41) 6x² – 17x – 3

= 6x² – 17x – 3

= 6x² – (18 – 1)x – 3

= 6x² – 18x + 1x – 3

= 6x(x – 3) + 1(x – 3)

= (x – 3) (6x + 1)

(42) 7x² – 19x – 6

= 7x² – (21 – 2)x – 6

= 7x² – 21x + 2x – 6

= 7x (x – 3) + 2(x – 3)

= (x – 3) (7x + 2)