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Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q20 . x2−y2−4xz+4z2

SOLUTION :

On rearranging the terms

= x2−4xz+4z2−y2

= (x)2−2×x×2z+(2z)2−y2

Using the identity x2−2xy+y2=(x−y)2

= (x−2z)2−y2

Using the identity  p2−q2= ( p + q )( p – q )

= (x−2z+y)(x−2z−y)

∴ x2−y2−4xz+4z= (x−2z+y)(x−2z−y)

 

Q21 .Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term ,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q22 .  Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics=Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q23 . Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q24 . Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q25 .Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics 

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q26 . Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q27 .  Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q28 .Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 SOLUTION :

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Using the identity  (x−y)2=x2+y2−2xy

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q29 .  Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

 

Q30 .Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

SOLUTION :

Splitting the middle term,

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics

Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics 

 

Q31 . 9(2a−b)2−4(2a−b)−13

SOLUTION :

Let  2a – b = x

=  9x2−4x−13

Splitting the middle term,

=  9x2−13x+9x−13

=  x(9x−13)+1(9x−13)

=  (9x−13)(x+1)

Substituting  x = 2a – b

=  [9(2a−b)−13](2a−b+1)

=  (18a−9b−13)(2a−b+1)

∴ 9(2a−b)2−4(2a−b)−13 = (18a−9b−13)(2a−b+1)

 

Q 32 . 7(x−2y)2−25(x−2y)+12

SOLUTION :

Let  x-2y = P

=  7P2−25P+12

Splitting the middle term,

=  7P2−21P−4P+12

=  7P(P−3)−4(P−3)

=  (P−3)(7P−4)

Substituting  P = x – 2y

=  (x−2y−3)(7(x−2y)−4)

=  (x−2y−3)(7x−14y−4)

∴ 7(x−2y)2−25(x−2y)+12 = (x−2y−3)(7x−14y−4)

 

Q33 . 2(x+y)2−9(x+y)−5

SOLUTION :

Let  x+y = z

=  2z2−9z−5

Splitting the middle term,

=  2z2−10z+z−5

=  2z(z−5)+1(z−5)

=  (z−5)(2z+1)

Substituting  z = x + y

=  (x+y−5)(2(x+y)+1)

=  (x+y−5)(2x+2y+1)

∴ 2(x+y)2−9(x+y)−5 = (x+y−5)(2x+2y+1)

 

Q34 . Give the possible expression for the  length  &  breadth of the rectangle having   35y2−13y−12 as its area.

SOLUTION :

Area is given as 35y2−13y−12

Splitting the middle term,

Area =  35y2+218y−15y−12

=  7y(5y+4)−3(5y+4)

=  (5y+4)(7y−3)

We also know that area of rectangle  = length ×breadth

∴ Possible length = (5y+4) and  breadth=(7y−3)

Or  possible length = (7y−3) and  breadth= (5y+4)

 

Q35 . What are  the possible expression for the cuboid having volume 3x2−12x.

SOLUTION :

Volume =  3x2−12x

= 3x(x−4)

= 3×x(x−4)

Also volume = Length ×Breadth×Height

∴ Possible expression for dimensions of cuboid are = 3 , x , (x−4)

The document Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on Ex-5.1, (Part - 2) Factorization Of Algebraic Expressions, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics

1. What is factorization of algebraic expressions?
Ans. Factorization of algebraic expressions is the process of breaking down an algebraic expression into its simpler and equivalent factors. It involves finding the common factors and expressing the given expression as a product of these factors.
2. Why is factorization important in algebra?
Ans. Factorization is important in algebra because it allows us to simplify complex expressions, solve equations, and find the roots of polynomial equations. It helps in understanding the structure of an expression and enables us to manipulate it more easily.
3. How do you factorize an algebraic expression?
Ans. To factorize an algebraic expression, we look for common factors and use various methods such as grouping, difference of squares, perfect square trinomials, and the quadratic formula. By applying these methods, we can break down the expression into its simpler factors.
4. What are the benefits of learning factorization of algebraic expressions?
Ans. Learning factorization of algebraic expressions helps in simplifying complex expressions, solving equations, and finding the roots of polynomial equations. It enhances problem-solving skills, improves understanding of algebraic concepts, and lays a strong foundation for higher-level mathematics.
5. Can you provide an example of factorization of an algebraic expression?
Ans. Sure! Let's factorize the expression 3x^2 + 9x. We can first find the common factor, which is 3x. Dividing the expression by this common factor, we get: 3x^2 + 9x = 3x(x + 3) So, the factorization of the given expression is 3x(x + 3).
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