In this chapter, we provide RD Sharma Solutions forClass 9 Chapter 5 Factorisation of Algebraic Expressions Ex 5.1 for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 9 Chapter 5 Factorisation of Algebraic Expressions Ex 5.1 pdf, free RD Sharma Solutions for Class 9 Chapter 5 Factorisation of Algebraic Expressions Ex 5.1 book pdf download. Now you will get step by step solution to each question.

## Factorisation of Algebraic Expressions RD Sharma Class 9 Solutions

### RD Sharma Class 9 Chapter 5 Factorisation of Algebraic Expressions Ex 5.1

Factorize

Question 1.

x^{3} + x – 3x^{2} – 3

Solution:

x^{3} + x – 3x^{2} – 3

x^{3} – 3a^{2} + x – 3

⇒ x^{2}(x – 3) + 1(x – 3)

= (x – 3) (x^{2} + 1)

Question 2.

a(a + b)^{3} – 3a^{2}b(a + b)

Solution:

a(a + b)^{3} – 3a^{2}b(a + b)

= a(a + b) {(a + b)^{2} – 3ab}

= a(a + b) {a^{2} + b^{2} + 2ab – 3ab}

= a{a + b) {a^{2} – ab + b^{2})

Question 3.

x(x^{3} – y^{3}) + 3xy(x – y)

Solution:

x(x^{3} – y^{3}) + 3xy(x – y)

= x(x – y) (x^{2} + xy + y^{2}) + 3xy(x – y)

= x(x – y) (x^{2} + xy + y^{2} + 3y)

= x(x – y) (x^{2} + xy + y^{2} + 3y)

Question 4.

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

Solution:

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

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

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

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

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

Question 5.

x^{2} + y – xy – x

Solution:

x^{2} + y – xy – x

= x^{2}-x-xy + y = x(x- l)-y(*- 1)

= (x – 1) (x – y)

Question 6.

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})

Question 7.*6*ab – b^{2} + 12ac – 2bc

Solution:

6ab – b^{2} + 12ac – 2bc

= 6ab + 12ac – b^{2} – 2bc

= 6a(b + 2c) – b(b + 2c)

= (b + 2c) (6a – b)

Question 8.

x(x – 2) (x – 4) + 4x – 8

Solution:

x(x – 2) (x – 4) + 4x – 8

= x(x – 2) (x – 4) + 4(x – 2)

= (x – 2) [x(x – 4) + 4]

= (x – 2) (x^{2} – 4x + 4)

= (x – 2) [(x)^{2} – 2 x x x 2 + (2)^{2}]

= (x – 2) (x – 2)^{2} = (x – 2)^{3}

Question 9.

(a – b + c)^{2} + (b – c + a)^{2} + 2(a – b + c) (b – c + a)

Solution:

(a – b + c)^{2} + ( b- c+a)^{2} + 2(a – b + c) (b – c + a) {∵ a^{2} + b^{2} + 2ab = (a + b)^{2}}

= [a – b + c + b- c + a]^{2}= (2a)^{2} = 4a^{2}

Question 10.

a^{2} + 2ab + b^{2} – c^{2}

Solution:

a^{2} + 2ab + b^{2} – c^{2}= (a^{2} + 2ab + b^{2}) – c^{2}= (a + b)^{2} – (c)^{2 }{∵ a^{2} – b^{2} = (a + b) (a – b)}

= (a + b + c) (a + b – c)

Question 11.

a^{2} + 4b^{2} – 4ab – 4c^{2}

Solution:

Question 12.

x^{2} – y^{2} – 4xz + 4z^{2}Solution:

x^{2} – y^{2} – 4xz + 4z^{2}= x^{2} – 4xz + 4z^{2} – y^{2}= (x)^{2} – 2 x x x 2z + (2z)^{2} – (y)^{2}= (x – 2z)^{2} – (y)^{2}= (x – 2z + y) (x – 2z – y)

= (x +y – 2z) (x – y – 2z)

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Give possible expression for the length and breadth of the rectangle having 35y^{2} + 13y – 12 as its area.

Solution:

Area of a rectangle = 35y^{2} + 13y – 12

= 35y^{2} + 28y- 15y- 12

(i) If length = 5y + 4, then breadth = 7y – 3

(ii) and if length = 7y-3, then length = 5y+ 4

Question 17.

What are the possible expressions for the dimensions of the cuboid whose volume is 3x^{2} – 12x.

Solution:

Volume 3x^{2} – 12x

= 3x(x – 4)

∴ Factors are 3, x, and x – 4

Now, if length = 3, breadth = x and height = x – 4

if length =3, breadth = x – 4, height = x

if length = x, breadth = 3, height = x – 4

if length = x, breadth = x – 4, height = 3

if length = x – 4, breadth = 3, height = x

if length – x – 4, breadth = x, height = 3

Question 18.

Solution:

Question 19.

(x + 2) (x^{2} + 25) – 10x^{2} – 20x

Solution:

(x + 2) (x^{2} + 25) – 10x^{2} – 20x

= (x + 2) (x^{2} + 25) – 10x(x + 2)

= (x + 2) [x^{2} + 25 – 10x]

= (x + 2) [(x)^{2} – 2 x x x 5 + (5)^{2}]

= (x + 2) (x – 5)^{2}

Question 20.

2a^{2} + 2(sqrt { 6 } ) ab +3b^{2}Solution:

2a^{2} + 2(sqrt { 6 } ) ab +3 b^{2}= ((sqrt { 2 } ) a)^{2}+ (sqrt { 2 } ) a x (sqrt { 3 } ) b+ ((sqrt { 3 } ) b)^{2}= ((sqrt { 2 } )a + (sqrt { 3 } ) b)^{2}

Question 21.

a^{2} + b^{2} + 2(ab + bc + ca)

Solution:

a^{2} + b^{2} + 2(ab + bc + ca)

= a^{2} + b^{2} + 2 ab + 2 bc + 2 ca

= (a + b)^{2} + 2c(b + a)

= (a + b)^{2} + 2c(a + b)

= (a + b) (a + b + 2c)

Question 22.

4(x – y)^{2} – 12(x -y) (x + y) + 9(x + y)^{2}Solution:

4(x – y)^{2} – 12(x – y) (x + y) + 9(x + y)^{2}= [2(x – y)^{2} + 2 x 2(x – y) x 3(x + y) + [3 (x+y]^{2 }{∵ a^{2} + b^{2} + 2 abc = (a + b)^{2}}

= [2(x – y) + 3(x + y)]^{2}= (2x-2y + 3x + 3y)^{2}

= (5x + y)^{2}

Question 23.

a^{2} – b^{2} + 2bc – c^{2}

Solution:

a^{2} – b^{2} + 2bc – c^{2}= a^{2} – (b^{2} – 2bc + c^{2}) {∵ a^{2} + b^{2} – 2abc = (a – b)^{2}}

= a^{2} – (b – c)^{2}= (a)^{2} – (b – c)^{2 }{∵ a^{2} – b^{2} = (a + b) (a – b)}

= (a + b – c) (a – b + c)

Question 24.

xy^{9} – yx^{9}Solution:

xy^{9} – yx^{9} = xy(y^{8} – x^{8})

= -xy(x^{8} – y^{8})

= -xy[(x^{4})^{2} – (y^{4})^{2}]

= -xy (x^{4} + y^{4}) (x^{4} – y^{4}) {∵ a^{2}-b^{2} = (a + b) (a – b)}

= -xy (x^{4} + y^{4}) {(x^{2})^{2} – (y^{2})^{2}}

= -xy(x^{4 }+ y^{4}) (x^{2} + y^{2}) (x^{2} – y^{2})

= -xy (x^{4} +y^{4}) (x^{2} + y^{2}) (x + y) (x -y)

= -xy(x – y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4})

Question 25.

x^{4} + x^{2}y^{2} + y^{4}Solution:

x^{4} + x^{2}y^{2} + y^{4} = (x^{2})^{2} + 2x^{2}y^{2} + y^{4} – x^{2}y^{2 }(Adding and subtracting x^{2}y^{2})

= (x^{2} + y^{2})^{2} – (xy)^{2 }{∵ a^{2} – b^{2} = (a + b) (a – b)}

= (x^{2} + y^{2} + xy) (x^{2} + y^{2} – xy)

= (x^{2} + xy + y^{2}) (x^{2} – xy + y^{2})

Question 26.

x^{2} + 6(sqrt { 2 } )x + 10

Solution:

Question 27.

x^{2} + 2(sqrt { 2 } )x- 30

Solution:

Question 28.

x^{2} – (sqrt { 3 } )x – 6

Solution:

Question 29.

x^{2} + 5 (sqrt { 5 } )x + 30

Solution:

Question 30.

x^{2} + 2 (sqrt { 3 } )x – 24

Solution:

Question 31.

5 (sqrt { 5 } )x^{2} + 20x + 3(sqrt { 5 } )

Solution:

Question 32.

2x^{2} + 3(sqrt { 5 } ) x + 5

Solution:

Question 33.

9(2a – b)^{2} – 4(2a – b) – 13

Solution:

Question 34.

7(x-2y) – 25(x-2y) +12

Solution:

Question 35.

2(x+y) – 9(x+y) -5

Solution:

2(x+y) – 9(x+y) -5

### Factorisation of Algebraic Expressions RD Sharma Class 9 Solutions Chapter 5 Exercise-5.1

Factorisation of Algebraic Expressions RD Sharma Class 9 Solutions Chapter 5 Exercise-5.1 Q 1.

**All Chapter RD Sharma Solutions For Class 9 Maths**

*************************************************

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also sharencertsolutionsfor.com to your friends.