Q. 10 B5.0( 1 Vote )

Verify that:

27a3 + b3 + c3 – 9abc = (3a + b + c)[3a2 + b2 + c2 – 3ab – bc – 3ac]

Answer :

Taking L.H.S

27a3 + b3 + c3 – 9abc = (3a)3 + b3 + c3 – 3(3a)(b)(c)


Using identity:


x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx)


27a3 + b3 + c3 – 9abc = (3a + b + c)((3a)2 + b2 + c2 – 3ab – bc – c(3a))


= (3a + b + c)[3a2 + b2 + c2 – 3ab – bc – 3ac]


= R.H.S


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Smart Revision | Polynomials IdentitiesSmart Revision | Polynomials IdentitiesSmart Revision | Polynomials Identities39 mins
Polynomials - Zero to HeroPolynomials - Zero to HeroPolynomials - Zero to Hero42 mins
Genius Quiz | PolynomialsGenius Quiz | PolynomialsGenius Quiz | Polynomials40 mins
Zeros and Degrees of a PolynomialZeros and Degrees of a PolynomialZeros and Degrees of a Polynomial41 mins
Genius Quiz |  Division of Algebraic ExpressionsGenius Quiz |  Division of Algebraic ExpressionsGenius Quiz | Division of Algebraic Expressions37 mins
Champ Quiz | PolynomialsChamp Quiz | PolynomialsChamp Quiz | Polynomials29 mins
Quiz | Imp. Qs. on Algebraic IdentitiesQuiz | Imp. Qs. on Algebraic IdentitiesQuiz | Imp. Qs. on Algebraic Identities65 mins
Basic understanding of PolynomialsBasic understanding of PolynomialsBasic understanding of Polynomials37 mins
Introduction to PolynomialsIntroduction to PolynomialsIntroduction to Polynomials37 mins
Methods to find zeroes of a Polynomial-2Methods to find zeroes of a Polynomial-2Methods to find zeroes of a Polynomial-246 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
caricature
view all courses