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

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

**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.**

**9x ^{2} + 12 xy**

**Solution:**

9x

^{2}+ 12xy

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

**Question 2.**

**18x ^{2}y – 24xyz**

**Solution:**

18x

^{2}y – 24xyz

= 6xy (3x – 4z) Ans.

**Question 3.**

**27a ^{3}b^{3} – 45a^{4}b^{2}**

**Solution:**

27a

^{3}b

^{3}– 45a

^{4}b

^{2}

= 9a

^{3}b

^{2}(3b – 5a) Ans.

**Question 4.**

**2a (x + y) – 3b(x + y)**

**Solution:**

2a (x + y) – 3b(x + y)

= (x + y) (2a – 3b) Ans.

**Question 5.**

**2x (p ^{2} + q^{2}) + 4y (p^{2} + q^{2})**

**Solution:**

2x (p

^{2}+ q

^{2}) + 4y (p

^{2}+ q

^{2})

= 2(p

^{2}+ q

^{2}) (x + 2y) Ans

**Question 6.**

**x (a – 5) + y (5 – a)**

**Solution:**

x (a – 5) + y (5 – a)

= x (a – 5) -y (a – 5)

= (a – 5) (x – y) Ans.

**Question 7.**

**4(a + b) – 6 (a + b) ^{2}**

**Solution:**

4(a + b) – 6 (a + b)

^{2}

= 2(a + b) {2 – 3 (a + b)}

= 2(a + b) (2 – 3a – 3b) Ans.

**Question 8.**

**8(3a – 2b) ^{2} – 10 (3a – 2b)**

**Solution:**

8(3a – 2b)

^{2}– 10 (3a – 2b)

= 2(3a – 2b) {4 (3a – 2b) – 5}

= 2(3a – 2b) (12a – 8b – 5) Ans.

**Question 9.**

**x (x + y) ^{3} – 3x^{2} y (x + y)**

**Solution:**

x (x + x)

^{3}– 3x

^{2}y (x + y)

= x (x + y) {(x + y)

^{2}– 3xy}

= x (x + y) [x

^{2}+ y

^{2}+ 2xy – 3xy)

= x (x + y) (x

^{2}+ y

^{2}– xy) Ans.

**Question 10.**

**x ^{3 }+ 2x^{2} + 5x + 10**

**Solution:**

x

^{3}+ 2x

^{2}+ 5x + 10

= x

^{2}(x + 2) + 5 (x + 2)

= (x + 2) (x

^{2}+ 5) Ans.

**Question 11.**

**x ^{2} + xy – 2xz – 2yz**

**Solution:**

x

^{2}+ xy – 2xz – 2yz

= x (x + y) -2z (x + y)

= (x + y) (x – 2z) Ans.

**Question 12.**

**a ^{3}b – a^{2}6 + 5ab – 5b**

**Solution:**

a

^{3}b – a

^{2}b + 5ab – 5b.

= b (a

^{3}– a

^{2}+ 5a – 5)

= b {(a

^{2}(a – 1) + 5 (a – 1)}

= b (a – 1) (a

^{2}+ 5) Ans.

**Question 13.**

**8 – 4a – 2a ^{3} + a^{4}**

**Solution:**

8 – 4a – 2a

^{3}+ a

^{4}

= 4 (2 – a) – a

^{3}(2 – a)

= (2 – a) (4 – a

^{3}) Ans.

**Question 14.**

**x ^{3} – 2x^{2}y + 3xy^{2} – 6y^{3}**

**Solution:**

x

^{3}– 2x

^{2}y + 3xy

^{2}– 6y

^{3}

= x

^{2}(x – 2y) + 3y

^{2}(x – 2y)

= (x – 2y) (x

^{2}+ 3y

^{2}) Ans

**Question 15.**

**px – 5q + pq – 5x**

**Solution:**

px – 5q + pq – 5x

= px – 5x + pq – 5q

= x(p – 5) + q(p – 5)

= {p – 5) (x + q) Ans.

**Question 16.**

**x ^{2} + y – xy – x**

**Solution:**

x

^{2}+ y – xy – x

= x

^{2}– x – xy + y

= x (x – 1) – y (x – 1)

= (x – 1) (x – y) Ans.

**Question 17.**

**(3a – 1) ^{2} – 6a + 2**

**Solution:**

(3a – 1)

^{2}– 6a + 2

= (3a – 1)

^{2}– 2 (3a – 1)

= (3a – 1) (3a – 1 – 2)

= (3a – 1) (3a – 3)

= 3(3a – 1) (a – 1) Ans.

**Question 18.**

**(2x – 3) ^{2} – 8x + 12**

**Solution:**

(2x – 3)

^{2}– 8x + 12

= (2x – 3)

^{2}– 4(2x – 3)

= (2x – 3) (2x – 3 – 4)

= (2x – 3) (2x – 7) Ans.

**Question 19.**

**a ^{3} + a – 3a^{2} – 3**

**Solution:**

a3 + a – 3a2 – 3

= a3 – 3a2 + a – 3

= a2 (a – 3) + 1 (a – 3)

= (a – 3) (a2 + 1) Ans.

**Question 20.**

**3ax – 6ay – 8by + 4bx**

**Solution:**

3ax – 6ay – 8by + 4bx

= 3ax – 6ay + 4bx – 8by

= 3a (x – 2y) + 4b (x – 2y)

= (x – 2y) (3a + 4b) Ans

**Question 21.**

**abx ^{2} + a^{2}x + b^{2}x + ab**

**Solution:**

abx

^{2}+ a

^{2}x + b

^{2}x + ab

= ax (bx + a) + b (bx + a)

= (bx + a) (ax + b) Ans.

**Question 22.**

**x ^{3} – x^{2} + ax + x – a – 1**

**Solution:**

x

^{3}– x

^{2}+ ax + x – a – 1

= x

^{3}– x

^{2}+ ax – a + x – 1

= x

^{2}(x – 1) + a (x – 1) + 1 (x – 1)

= (x – 1) (x

^{2}+ a + 1) Ans.

**Question 23.**

**2x + 4y – 8xy – 1**

**Solution:**

2x + 4y – 8xy – 1

= 2x – 8xy -1+4y

= 2x (1 – 4y) -1 (1 – 4y)

= (1 – 4y) (2x – 1) Ans.

**Question 24.**

**ab (x ^{2} + y^{2}) – xy (a^{2} + b^{2})**

**Solution:**

ab (x

^{2}+y

^{2}) – xy (a

^{2}+ b

^{2})

= abx

^{2}+ aby

^{2}– a

^{2}xy – b

^{2}xy

= abx

^{2}– a

^{2}xy – b

^{2}xy + aby

^{2}

= ax (bx – ay) – by (bx – ay)

= (bx – ay) (ax – by) Ans.

**Question 25.**

**a ^{2} + ab (b + 1) + b^{3}**

**Solution:**

a

^{2}+ ab (b + 1) + b

^{3}

= a

^{2}+ ab

^{2}+ ab + b

^{3}

= a (a + b

^{2}) + b (a + b

^{2})

= (a + b

^{2}) (a + b) Ans

**Question 26.**

**a ^{3} + ab (1 – 2a) – 2b^{2}**

**Solution:**

a

^{3}+ ab (1 – 2a) – 2b

^{2}

= a

^{3}+ ab – 2a

^{2}b – 2b

^{2}

= a

^{3}– 2a

^{2}b + ab – 2b

^{2}

= a

^{2}(a – 2b) + b (a – 2b)

= (a – 2b) (a

^{2}+ b) Ans.

**Question 27.**

**2a ^{2} + bc – 2ab – ac**

**Solution:**

2a

^{2}+ bc – 2ab – ac

= 2a

^{2}– 2ab – ac + bc

= 2a (a – b) – c (a – b)

= (a – b) (2a – c) Ans.

**Question 28.**

**(ax + by) ^{2} + (bx – ay)^{2}**

**Solution:**

(ax + by)

^{2}+ (bx – ay)

^{2}

= a

^{2}x

^{2}+ b

^{2}y

^{2}+ 2abxy + b

^{2}x

^{2}+ a

^{2}y

^{2}– 2bxy

= a

^{2}x

^{2}+ b

^{2}y

^{2}+ b

^{2}x

^{2}+ a

^{2}y

^{2}

= a

^{2}x

^{2}+ b

^{2}x

^{2}+ a

^{2}y

^{2}+ b

^{2}y

^{2}

= x2(a2 + b2) + y2(a2 + b2)

= (a

^{2}+ b

^{2}) (x

^{2}+ y

^{2}) Ans.

**Question 29.**

**a (a + b – c) – bc**

**Solution:**

a (a + b – c) – bc

= a^{2} + ab – ac – bc

= a (a + b) – c (a + b)

(a + b) (a – c) Ans.

**Question 30.**

**a(a – 2b – c) + 2bc**

**Solution:**

a(a – 2b – c) + 2bc

= a^{2} – 2ab – ac +2bc

= a^{2} – ac – 2ab + 2bc

= a (a – c) – 2b (a – c)

= (a – c) (a – 2b) Ans.

**Question 31.**

**a ^{2}x^{2} + (ax^{2} + 1) x + a**

**Solution:**

a

^{2}x

^{2}+ (ax

^{2}+ 1) x + a

= a

^{2}x

^{2}+ ax

^{3}+ x + a

= a

^{2}x

^{2}+ ax

^{3}+ a + x

= ax

^{2}(a + x) + 1 (a + x)

– (a + x) (ax

^{2}+ 1) Ans

**Question 32.**

**ab (x ^{2} + 1) + x (a^{2} + b^{2})**

**Solution:**

ab (x

^{2}+ 1) + x (a

^{2}+ b

^{2})

= abx

^{2}+ ab + a

^{2}x + b

^{2}x

= abx

^{2}+ a

^{2}x + b

^{2}x + ab

= ax (bx + a) + b (bx + a)

= (bx + a) (ax + b) Ans.

**Question 33.**

**x ^{2} – (a + b) x + ab**

**Solution:**

x

^{2}– (a + b) x + ab

= x

^{2}– ax – bx + ab

= x (x – a) – b (x – a)

= (x – a) (x – b) Ans.

**Question 34.**

**Solution:**

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

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