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

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**Q20 . x ^{2}−y^{2}−4xz+4z^{2}**

**SOLUTION :**

On rearranging the terms

= x^{2}−4xz+4z^{2}−y^{2}

= (x)^{2}−2×x×2z+(2z)^{2}−y^{2}

Using the identity x^{2}−2xy+y^{2}=(x−y)^{2}

= (x−2z)^{2}−y^{2}

Using the identity p^{2}−q^{2}= ( p + q )( p – q )

= (x−2z+y)(x−2z−y)

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

**Q21 .**

**SOLUTION :**

Splitting the middle term ,

**Q22 . **

**SOLUTION :**

Splitting the middle term,

=

**Q23 . **

**SOLUTION :**

Splitting the middle term,

**Q24 . **

**SOLUTION :**

Splitting the middle term,

**Q25 .**

**SOLUTION :**

Splitting the middle term,

**Q26 . **

**SOLUTION :**

Splitting the middle term,

**Q27 . **

**SOLUTION :**

Splitting the middle term,

**Q28 .**

** SOLUTION :**

Using the identity (x−y)^{2}=x^{2}+y^{2}−2xy

**Q29 . **

**SOLUTION :**

Splitting the middle term,

**Q30 .**

**SOLUTION :**

Splitting the middle term,

**Q31 . 9(2a−b) ^{2}−4(2a−b)−13**

**SOLUTION :**

Let 2a – b = x

= 9x^{2}−4x−13

Splitting the middle term,

= 9x^{2}−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,

= 7P^{2}−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 35y ^{2}−13y−12 as its area.**

**SOLUTION :**

Area is given as 35y^{2}−13y−12

Splitting the middle term,

Area = 35y^{2}+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 3x ^{2}−12x.**

**SOLUTION :**

Volume = 3x^{2}−12x

= 3x(x−4)

= 3×x(x−4)

Also volume = Length ×Breadth×Height

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