## RS Aggarwal Class 8 Solutions Chapter 7 Factorisation Ex 7D

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7D.

**Other Exercises**

- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7A
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7B
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7C
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7D
- RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7E

**Question 1.**

**Solution:**

x^{2} + 5x + 6

= x^{2} + 2x + 3x + 6

{6 = 2 x 3, 5 = 2 + 3}

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

= (x + 2) (x + 3) Ans.

**Question 2.**

**Solution:**

y^{2} + 10y + 24

= y^{2} + 6y + 4y + 24

{24 = 6 x 4, 10 = 6 + 4}

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

= (y + 6) (y + 4)

**Question 3.**

**Solution:**

z^{2} + 12x + 27

{27 = 9 x 3, 12 = 9 + 3}

= z^{2} + 9z + 3z + 27

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

= (z + 9) (z + 3)

**Question 4.**

**Solution:**

p^{2} + 6p + 8

= p^{2} + 4p + 2p + 8

{ 8 = 4 x 2, 6 = 4 + 2}

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

= (p + 4) (p + 2)

**Question 5.**

**Solution:**

x^{2} + 15x + 56

= x^{2} + 8x + 7x + 56

{56 = 8 x 7, 15 = 8 x 7}

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

= (x + 8) (x + 7) Ans.

**Question 6.**

**Solution:**

y^{2} + 19y + 60

= y^{2} + 15y + 4y + 60

{60 = 15 x 4, 19 = 15 + 4}

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

= (y + 15) (y + 4)

**Question 7.**

**Solution:**

x^{2} + 13x + 40

= x^{2} + 5x + 8x + 40

{40 = 5 x 8, 13 = 5 + 8}

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

= (x + 5) (x + 8) Ans.

**Question 8.**

**Solution:**

q^{2} – 10q + 21

= q^{2} – 7q – 3q + 21

{21 = ( – 7)x( – 3), – 10 = – 7 – 3}

= q {q – 7) – 3 (q – 7)

= (q – 7)(q – 3)

**Question 9.**

**Solution:**

p^{2 }+ 6p – 16

= p^{2} + 8p – 2p – 16

{ – 16 = 8x( – 2),6 = 8 – 2}

= p (p + 8) – 2 (p + 8)

= (p + 8) (p – 2)

**Question 10.**

**Solution:**

x^{2} – 10x + 24

= x^{2} – 6x – 4x + 24

{24 = ( – 6) x ( – 4), – 10 = – 6 – 4 }

= x(x – 6) – 4(x – 6)

= (x – 6) (x – 4) Ans.

**Question 11.**

**Solution:**

x^{2} – 23x + 42

= x^{2} – 2x – 21x + 42

{42 = ( – 2) x ( – 21), – 23 = – 2 – 21}

= x(x – 2) – 21(x – 2)

= (x – 2) (x – 21) Ans.

**Question 12.**

**Solution:**

x^{2} – 17x + 16

= x^{2} – x – 16x + 16

{ 16 = ( – 1) x ( – 16), 17 = – 1 – 16}

= x (x – 1) – 16(x – 1)

= (x – 1) (x – 16) Ans.

**Question 13.**

**Solution:**

y^{2} – 21y + 90

= y^{2} – 15y – 6y + 90

{90 = ( – 15)x ( – 6), – 21 = – 15 – 6}

= y(y – 15) – 6 (y – 15)

= (y – 15) (y – 6)

**Question 14.**

**Solution:**

x^{2} – 22x + 117

= x^{2} – 13x – 9x + 117

{117 = ( – 13) x ( – 9), – 22 = – 13 – 9}

= x(x – 13) – 9(x – 13)

= (x – 9) (x – 13) Ans.

**Question 15.**

**Solution:**

x^{2} – 9x + 20

= x^{2} – 5x – 4x + 20

{ 20 = ( – 5) x ( – 4), – 9 = – 5 – 4}

= x(x – 5) – 4(x – 5)

= (x – 5) (x – 4) Ans.

**Question 16.**

**Solution:**

x^{2} + x – 132

= x^{2} + 12x – 11x – 132

{ – 132 = 12 x ( – 11), 1 = 12 – 11}

= x(x + 12) – 11(x + 12)

= (x + 12) (x – 11) Ans.

**Question 17.**

**Solution:**

x^{2} + 5x – 104

= x^{2} + 13x – 8x – 104

{ – 104 = 13 x ( – 8), 5 = 13 – 8}

= x(x + 13) – 8(x + 13)

= (x + 13) (x – 8) Ans.

**Question 18.**

**Solution:**

y^{2} + 7y – 144

= y^{2} + 16y – 9y – 144

{144 = – 16 x 9, 7 = 16 – 9}

= y(y +16) – 9(y + 16)

= (y + 16) (y – 9) Ans.

**Question 19.**

**Solution:**

z^{2} + 19z – 150

= z^{2} + 25z – 6z – 150

{ – 150 = 25 x ( – 6), 19 = 25 – 6}

= z(z + 25) – 6(z + 25)

= (z + 25) (z – 6) Ans.

**Question 20.**

**Solution:**

y^{2} + y – 72

= y^{2} + 9y – 8y – 72

{ – 72 = 9x( – 8), 1 = 9 – 8}

= y(y + 9) – 8(y + 9)

= (y + 9) (y – 8) Ans

**Question 21.**

**Solution:**

a^{2} + 6a – 91

= a^{2} + 13a – 7a – 91

{ – 91 = 13x( – 7), 6 = 13 – 7}

= a (a + 13) – 7 (a + 13)

= (a + 13) (a – 7)

**Question 22.**

**Solution:**

p^{2} – 4p – 11

= p^{2} – 11p + 7p – 77

{ – 77 = – 11 x 7, – 4 = – 11 + 7}

= p(p – 11) + 7 (p – 11)

= (p – 11)(p + 7)

**Question 23.**

**Solution:**

x^{2} – 7x – 30

= x^{2} – 10x + 3x – 30

{ – 30 = – 10 x 3, – 7 = – 10 + 3}

= x(x – 10) + 3(x – 10)

= (x – 10) (x + 3) Ans.

**Question 24.**

**Solution:**

x^{2} – 14 x + 3 x – 42

{ – 11 = – 14 + 3], – 42 = – 14 x 3}

= x (x – 14) + 3 (x – 14)

= (x – 14) (x + 3) Ans.

**Question 25.**

**Solution:**

x^{2} – 5x – 24

= x^{2} – 8x + 3x – 24

{ – 24 = – 8 x 3, – 5 = – 8 + 3}

= x(x – 8) + 3(x – 8)

= (x – 8) (x + 3) Ans.

**Question 26.**

**Solution:**

y^{2} – 6y – 135

= y^{2} – 15y + 9y – 135

{ – 135 = – 15 x 9, – 6 = – 15 + 9}

= y (y – 15) + 9 (y – 15)

= (y – 15) (y + 9)

**Question 27.**

**Solution:**

z^{2} – 12z – 45

= z^{2} – 15z + 3z – 45

= z (z – 15) + 3 (z – 15)

{ – 45 = – 15 x 3, – 12 = – 15 + 3}

= (z – 15)(z + 3)

**Question 28.**

**Solution:**

x^{2} – 4x – 12

= x^{2} – 6x + 2x – 12

{ – 12 = – 6 x 2, – 4 = – 6 + 2}

= x (x – 6) + 2 (x – 6)

= (x – 6) (x + 2)

**Question 29.**

**Solution:**

3x^{2} + 10x + 8

= 3x^{2} + 6x + 4x + 8

{ 3 x 8 = 24, 24 = 6 x 4,10 = 6 + 4}

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

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

**Question 30.**

**Solution:**

3y^{2} + 14y + 8

= 3y^{2} + 12y + 2y + 8

{3 x 8 = 24, 24 = 12 x 2, 14 = 12 + 2}

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

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

**Question 31.**

**Solution:**

3z^{2} – 10z + 8

= 3z^{2} – 6z – 4z + 8

{ 3 x 8 = 24, 24 = ( – 6)x( – 4), – 10 = – 6 – 4}

= 3z (z – 2) – 4 (z – 2)

= (z – 2) (3z – 4)

**Question 32.**

**Solution:**

2x^{2} + x – 45

= 2x^{2} + 10x – 9x – 45

{2 x ( – 45) = – 90,- 90 = (10)x( – 9), 1 = 10 – 9}

= 2x (x – 5) + 9 (x – 5)

= (x – 5) (2x + 9)

**Question 33.**

**Solution:**

6p^{2} + 11p – 10

= 6x^{2} + 15x – 4x – 10

{6x ( – 10) = 60, – 60 = 15 x ( – 4),11 = 15 – 4}

= 3x (2x + 5) – 2 (2x + 5)

= (3x – 2) (2x + 5) Ans.

**Question 34.**

**Solution:**

2x^{2} – 20x + 3x – 30

{2 x ( – 30) = – 60, – 17 = – 20 + 3, – 60 = – 20 x 3}

= 2x (x – 10) + 3 (x – 10)

= (x – 10) (2x + 3) Ans.

**Question 35.**

**Solution:**

7y^{2} -19y – 6

= 7y^{2} – 21 y + 2y – 6

{7 x ( – 6) = – 42, – 42 = – 21 x 2, – 19 = – 21 + 2}

= 7y(y – 3) + 2 (y – 3)

= (y – 3) (7y + 2)

**Question 36.**

**Solution:**

28 – 31x – 5x^{2}

= 28 – 35x + 4x – 5x^{2}

{28 x ( – 5)= – 140, -140 = – 35 x 4, – 31 = – 35 + 4}

= 7 (4 – 5x) + x (4 – 5x)

= (4 – 5x) (7 + x)

**Question 37.**

**Solution:**

3 + 23z – 8z^{2}

= 3 + 24z – z – 8z^{2}

{3 x ( – 8) = – 24, – 24 = 24 x ( – 1), 23 = 24 – 1}

= 3 (1 + 8z) – z (1 + 8z)

= (1 + 8z) (3 – z)

**Question 38.**

**Solution:**

6x^{2} – 5x – 6

= 6x^{2} – 9x + 4x – 6

{ 6 x ( – 6) = – 36,- 36 = – 9 x 4, – 5 = – 9 + 4}

= 3x (2x – 3) + 2 (2x – 3)

= (2x – 3) (3x + 2)

**Question 39.**

**Solution:**

3m^{2} + 24m + 36

= 3 {m^{2} + 8m + 12}

= 3 {m^{2} + 6m + 2m + 12)

{12 = 6 x 2, 8 = 6 + 2}

= 3 {m (m + 6) + 2 (m + 6)}

= 3 (m + 6) (m + 2)

**Question 40.**

**Solution:**

4n^{2} – 8n + 3

= 4n^{2} – 6n – 2n + 3

{4 x 3 = 12, 12 = ( – 6)x( – 2), – 8 = – 6 – 2}

= 2n (2n – 3) – 1 (2n- 3)

= (2n – 3) (2n – 1)

**Question 41.**

**Solution:**

6x^{2} – 17x – 3

= 6x^{2} – 18x + x – 3

{6 x ( – 3)= – 18, – 18 = – 18 x 1, – 17 = – 18 + 1}

= 6x (x – 3) + 1 (x – 3)

= (x – 3) (6x + 1)

**Question 42.**

**Solution:**

7x^{2} – 19x – 6

7x^{2} – 19x – 6

= 7x^{2} – 21x + 2x – 6

{7 x ( – 6) = – 42, – 42 = – 21 x 2, – 19 = – 21 + 2}

= 7x (x – 3) + 2 (x – 3)

= (x – 3) (7x + 2)

Hope given RS Aggarwal Solutions Class 8 Chapter 7 Factorisation Ex 7D are helpful to complete your math homework.

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