# Factorize each of the following:(i) (ii) (iii) (iv) (v)

(i)
Using identity,

(a + b)3 = a3 + b3 + 3a2b + 3ab2

8a3 + b3 + 12a2b + 6ab2

= (2a)3 + b3 + 3 (2a) (2b) + 3 (2a) (b)2

= (2a + b)3

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

(ii)
Using identity,

(a + b)3 = a3 + b3 + 3a2b + 3ab2

8a3 – b3 – 12a2b + 6ab2

= (2a)3 – b3 – 3 (2a)2b + 3 (2a) (b)2

= (2a – b)3

= (2a – b) (2a – b) (2a – b)

(iii)
Using identity,

(a - b)3 = a3 - b3 - 3a2b + 3ab2

27 – 125a3 – 135a + 225a2

= 33 – (5a)3 – 3 (3)2(5a) + 3 (3) (5a)2

= (3 – 5a)3

= (3 – 5a) (3 – 5a) (3 – 5a)

(iv)
Using identity,

(a - b)3 = a3 - b3 - 3a2b + 3ab2

64a3 – 27b3 – 144a2b + 108ab2

= (4a)3 – (3b)3 – 3 (4a)2 (3b) + 3 (4a) (3b)2

= (4a – 3b)3

= (4a – 3b) (4a – 3b) (4a – 3b)

(v)
Using identity,

(a + b)3 = a3 + b3 + 3a2b + 3ab2

27p3 - - p2 + p

= (3p)3 – ()3 – 3 (3p)2 () + 3 (3p) ()2

= (3p - )3

= (3p - ) (3p - ) (3p - )

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Polynomials - Zero to Hero42 mins
Genius Quiz | Polynomials40 mins
Zeros and Degrees of a Polynomial41 mins
Genius Quiz | Division of Algebraic Expressions37 mins
Champ Quiz | Polynomials29 mins
Smart Revision | Polynomials Identities39 mins
Quiz | Imp. Qs. on Algebraic Identities65 mins
Basic understanding of Polynomials37 mins
Introduction to Polynomials37 mins
QUiz on Previous year NTSE Questions45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

75×75+2×75×25+25×25 equal to

RD Sharma - Mathematics

If x+ =5, then x2+=

RD Sharma - Mathematics

If a2+ =102, find the value of a-.

RD Sharma - Mathematics

Factorize:

2 – 50x2

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

100 – 9x2

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

10x2 – 9x – 7

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

9x2 + 16y2 + 4z2 –24xy + 16yz – 12xz

RS Aggarwal & V Aggarwal - Mathematics

If a1/3+b1/3 + c1/3 =0, then

RD Sharma - Mathematics

Factorize:

x2 – y2 + 6y – 9

RS Aggarwal & V Aggarwal - Mathematics

Factorize:

RS Aggarwal & V Aggarwal - Mathematics