If x + y + z = 0, show that: (cube of x) + (cube of y) + (cube of z) = 3xyz?

Asked by Last Modified  

Follow 0
Answer

Please enter your answer

Tuition at its Best

We know that, a 3 + b 3 + c 3=(a + b + c)(a 2 + b 2 + c 2 - ab - bc - ca) + 3abc. Substitute (a + b +c) = 0 in above equation: => a 3 + b 3 + c 3=0 x (a 2 + b 2 + c 2 - ab - bc - ca) + 3abc=>a 3 + b 3 + c 3 = 3abc.
Comments

Related Questions

Evaluate the product without multiplying directly: 103 x 107?
103 x 107 = (100 + 3)(100 + 7) We know that (x + a)(x + b) = x^2 + (a + b)x + ab Therefore, 103 x 107 = 100^2 + (3 + 7) x 100 + 3 x 7 = 10000 + 1000 + 21 = 11021
Shubham
0 0
6
Find the sum of: 5 + x - (square of x), 3x + 5 + 2(square of x)?
5+x-square of x+3x+5+2square of x =10+4x+(square of x)
Divya

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons


Be A Python Dev
Currently, in the programming world, Python is one of the languages with a high rising demand profile. And this article will explain why that isn’t slowing down in the foreseeable future.Python...

Algebraic Expressions and Identities - Key Points to Remember - [CBSE Class 8 Mathematics - Chapter 9]
Key Points to Remember 1. Algebraic Expressions Algebraic Expressions are formed from Variables and Constants. The expression '2p–5' is formed from the variable 'p' and constants '2' and '5'....


Recommended Articles

Learning for every child starts from a very young age. While the formal methods include school curriculums and private lessons, the informal methods include dancing, music, drawing, and various fun-filling activities. Playing games and practising these types of activities helps the children get out of boredom and...

Read full article >

Quality education does not only help children to get a successful career and life, but it also hugely contributes to society. The formal education of every child starts from school. Although there are numerous schools, parents find it challenging to choose the right one that would fit their child. It is difficult for them...

Read full article >

E-learning is not just about delivering lessons online. It has a much broader scope that goes beyond manual paper or PowerPoint Presentations. To understand the reach of E-learning and how the whole process works in developing the Educational system, we will discuss a few points here. Let us find out how this new learning...

Read full article >

Once over with the tenth board exams, a heavy percentage of students remain confused between the three academic streams they have to choose from - science, arts or commerce. Some are confident enough to take a call on this much in advance. But there is no worry if as a student you take time to make choice between - science,...

Read full article >

Looking for Class 8 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you