## 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.**

**Solution:**

25x^{2} – 64y^{2}

= (5x)^{2} – (8y)^{2}

= (5x + 8y) (5x – 8y) Ans.

**Question 2.**

**Solution:**

100 – 9x^{2}

(10)^{2} – (3x)^{2}

= (10 + 3x) (10 – 3x) Ans.

**Question 3.**

**Solution:**

5x^{2} – 7y^{2}

=(√5x)^{2} +(√7y)^{2}

=(√5x – √7y)(√5x – √7y) Ans

**Question 4.**

**Solution:**

(3x + 5y)^{2} – 4z^{2}

= (3x + 5y)^{2} – (2z)^{2}

= (3x + 5y + 2z) (3x + 5y – 2z) Ans.

**Question 5.**

**Solution:**

150 – 6x^{2}

= 6(25 – x^{2})

= 6{(5)^{2} – (x^{2})}

= 6 (5 + x) (5 – x) Ans.

**Question 6.**

**Solution:**

20x^{2} – 45

= 5 (4x^{2} – 9)

= 5{(2x)^{2} – (3)^{2}}

= 5 (2x + 3) (2x – 3) Ans.

**Question 7.**

**Solution:**

3x^{3} – 48x

= 3x (x^{2} – 16)

= 3x {(x)^{2} – (4)^{2}}

= 3x (x + 4) (x – 4) Ans.

**Question 8.**

**Solution:**

2 – 50x^{2}

= 2(1 – 25x^{2}) = 2 {(1)^{2} – (5x)^{2}}

= 2 (1 + 5x) (1 – 5x) Ans.

**Question 9.**

**Solution:**

27a^{2} – 48b^{2}

= 3(9a^{2} – 16b^{2})

= 3 {(3a)^{2} – (4b)^{2}}

= 3(3a + 4b) (3a – 4b) Ans.

**Question 10.**

**Solution:**

x – 64x^{3}

= x (1 – 64x^{2})

= x{(1)^{2} – (8x)^{2}}

= x (1 + 8x) (1 – 8x) Ans.

**Question 11.**

**Solution:**

8ab^{2} – 18a^{3}

= 2a (4b^{2} – 9a^{2})

= 2a {(2b)^{2} – (3a)^{2}}

= 2a (2b + 3a) (2b – 3a) Ans

**Question 12.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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.**

**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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