## RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2F

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F.

**Other Exercises**

- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2A
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2B
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2C
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2D
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2E
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2G
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2H
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2I
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2J
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2K

**Factorize :**

**Question 1.**

**25x ^{2}-64y^{2}**

**Solution:**

25x

^{2}– 64y

^{2}

= (5x)

^{2}– (8y)

^{2}

= (5x + 8y) (5x – 8y) Ans.

**Question 2.**

**100 – 9x ^{2}**

**Solution:**

100 – 9x

^{2}

(10)

^{2}– (3x)

^{2}

= (10 + 3x) (10 – 3x) Ans.

**Question 3.**

**5x ^{2}**

**-7y**

^{2}**Solution:**

5x

^{2}– 7y

^{2}

=(√5x)

^{2}+(√7y)

^{2}

=(√5x – √7y)(√5x – √7y) Ans

**Question 4.**

**(3x + 5y) ^{2} – 4z^{2}**

**Solution:**

(3x + 5y)

^{2}– 4z

^{2}

= (3x + 5y)

^{2}– (2z)

^{2}

= (3x + 5y + 2z) (3x + 5y – 2z) Ans.

**Question 5.**

**150 – 6x ^{2}**

**Solution:**

150 – 6x

^{2}

= 6(25 – x

^{2})

= 6{(5)

^{2}– (x

^{2})}

= 6 (5 + x) (5 – x) Ans.

**Question 6.**

**20x ^{2} – 45**

**Solution:**

20x

^{2}– 45

= 5 (4x

^{2}– 9)

= 5{(2x)

^{2}– (3)

^{2}}

= 5 (2x + 3) (2x – 3) Ans.

**Question 7.**

**3x ^{3} – 48x**

**Solution:**

3x

^{3}– 48x

= 3x (x

^{2}– 16)

= 3x {(x)

^{2}– (4)

^{2}}

= 3x (x + 4) (x – 4) Ans.

**Question 8.**

**2 – 50x ^{2}**

**Solution:**

2 – 50x

^{2}

= 2(1 – 25x

^{2}) = 2 {(1)

^{2}– (5x)

^{2}}

= 2 (1 + 5x) (1 – 5x) Ans.

**Question 9.**

**27a2 – 48b ^{2}**

**Solution:**

27a

^{2}– 48b

^{2}

= 3(9a

^{2}– 16b

^{2})

= 3 {(3a)

^{2}– (4b)

^{2}}

= 3(3a + 4b) (3a – 4b) Ans.

**Question 10.**

**x – 64x ^{3}**

**Solution:**

x – 64x

^{3}

= x (1 – 64x

^{2})

= x{(1)

^{2}– (8x)

^{2}}

= x (1 + 8x) (1 – 8x) Ans.

**Question 11.**

**8ab ^{2} – 18a^{3}**

**Solution:**

8ab

^{2}– 18a

^{3}

= 2a (4b

^{2}– 9a

^{2})

= 2a {(2b)

^{2}– (3a)

^{2}}

= 2a (2b + 3a) (2b – 3a) Ans

**Question 12.**

**3a ^{3}b – 243ab^{3}**

**Solution:**

3a

^{3}b – 243ab

^{3}

= 2ab (a

^{2}-81 b

^{2})

= 3ab {(a)

^{2}– (9b)

^{2}}

= 3ab (a + 9b) (a – 9b) Ans.

**Question 13.**

**(a + b) ^{3} – a – b**

**Solution:**

(a + b)

^{3}– a – b

= (a + b)

^{3}– 1 (a + b)

= (a + b) {(a + b)

^{2}– 1}

= (a + b) {(a + b)

^{2}– (1)

^{2}}

= (a + b) (a + b + 1) (a + b – 1) Ans.

**Question 14.**

**108 a ^{2} – 3(b – c)^{2}**

**Solution:**

108 a

^{2}– 3(b – c)

^{2}

= 3 {36a

^{2}– (b – c)

^{2}}

= 3 {(6a)

^{2}– (b – c)

^{2}}

= 3 {(6a + (b – c)} {6a – (b – c)}

= 3 (6a + b – c) (6a – b + c) Ans.

**Question 15.**

**x ^{3} – 5x^{2} – x + 5**

**Solution:**

x

^{3}– 5x

^{2}– x + 5

= x

^{2}(x – 5) -1(x – 5)

= (x – 5) (x

^{2}– 1)

= (x – 5) {(x)

^{2}– (1)

^{2}}

= (x – 5) (x + 1) (x – 1) Ans.

**Question 16.**

**a ^{2} + 2ab + b^{2} – 9c^{2}**

**Solution:**

a

^{2}+ 2ab + b

^{2}– 9c

^{2}

= (a + b)

^{2}– (3c)

^{2}

= {a

^{2}+ b

^{2}+ 2ab – (a + b)

^{2}}

= (a + b + 3c) (a + b – 3c) Ans.

**Question 17.**

**9 – a ^{2} + 2ab – b^{2}**

**Solution:**

9 – a

^{2}+ 2ab – b

^{2}

= 9 – (a

^{2}– 2ab + b

^{2})

= (3)

^{2}-(a- b)

^{2}

{ ∴a

^{2}+ b

^{2}– 2ab = (a – b)

^{2}}

= (3 + a – b) (3 – a + b) Ans.

**Question 18.**

**a ^{2} – b^{2} – 4ac + 4c^{2}**

**Solution:**

a

^{2 }– b

^{2}– 4ac + 4c

^{2}

= a

^{2}– 4ac + 4c

^{2}– b

^{2}

= (a)

^{2}– 2 x a x 2c + (2c)

^{2}– (b)

^{2}

= (a – 2c)

^{2}– (b)

^{2}

= (a – 2c + b) (a – 2c – b)

= (a + b – 2c) (a – b – 2c) Ans.

**Question 19.**

**9a ^{2} + 3a- 8b – 64b^{2}**

**Solution:**

9a

^{2}+ 3a – 8B – 64b

^{2}

= 9a

^{2}– 64b

^{2}+ 3a – 8b

= (3a)

^{2}– (8b)

^{2}+ 1(3a – 8b)

= (3a + 8b) (3a – 8b) + 1 (3a – 8b)

= (3a – 8b) (3a + 8b + 1) Ans.

**Question 20.**

**x ^{2} – y^{2} + 6y – 9**

**Solution:**

x

^{2}– y

^{2}+ 6y _ 9

= (x)2 – (y

^{2}– 6y + 9)

= (x)2 – {(y)

^{2}– 2 x y x 3 + (3)

^{2}}

= (x)

^{2}– (y – 3)

^{2}

= (x + y – 3) (x – y + 3) Ans.

**Question 21.**

**4x ^{2} – 9y^{2} -2x -3y**

**Solution:**

4x

^{2}– 9y

^{2}– 2x – 3y

= (2x)

^{2}– (3y)

^{2}– 1(2x + 3y)

= (2x + 3y) (2x – 3y) – 1( 2x + 3y)

= (2x + 3y) (2x – 3y – 1) Ans.

**Question 22.**

**x ^{4} – 1**

**Solution:**

x

^{4}– 1

= (x

^{2})

^{2}– (1)

^{2}

= (x

^{2}+ 1) (x

^{2}– 1)

= (x

^{2}+ 1) {(x)

^{2}– (1)

^{2}}

= (x

^{2}+ 1) (x + 1) (x – 1) Ans.

**Question 23.**

**a – b – a ^{2} + b^{2}**

**Solution:**

a – b – a

^{2}+ b

^{2}

= 1 (a – b) – (a

^{2}– b

^{2})

= 1 (a – b) – (a + b) (a – b)

= (a – b) (1 – a – b) Ans.

**Question 24.**

**x ^{4} – 625**

**Solution:**

**x**

^{4}– 625= (x

^{2})

^{2}– (25)

^{2}

= (x

^{2}+ 25) (x

^{2}– 25)

= (x

^{2}+ 25) {(x)

^{2}– (5)

^{2}}

= (x

^{2}+ 25) (x + 5) (x – 5) Ans.

Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F are helpful to complete your math homework.

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