Question Number 101514 by bemath last updated on 03/Jul/20

Commented by Dwaipayan Shikari last updated on 03/Jul/20

Commented by Rasheed.Sindhi last updated on 03/Jul/20

Commented by mr W last updated on 03/Jul/20

Commented by Rasheed.Sindhi last updated on 03/Jul/20

Answered by Rasheed.Sindhi last updated on 03/Jul/20

Commented by bemath last updated on 03/Jul/20

Answered by 1549442205 last updated on 07/Jul/20
![a^3 +b^3 +c^3 =(a+b)^3 −3ab(a+b)+c^3 −3abc =[(3−c)^3 +c^3 ]−3ab(a+b+c)= (3+c−c)[(3−c)^2 −(3−c)c+c^2 ]−9ab =3(9−6c+c^2 −3c+c^2 +c^2 )−9ab =3(9−9c+3c^2 )−9ab=9(c^2 −3c+3−ab) =9[c(−a−b)+3−ab]=9[3−(ab+bc+ca)] =9(−2+3)=9 other way:a^3 +b^3 +c^3 −3abc=(a+b+c)^3 −3(a+b)(a+c)(b+c)−3abc= 3^3 −3[(3−a)(3−b)(3−c)]−3abc= 27−3[27−9(a+b+c)+3(ab+bc+ca)−abc]−3abc =27−3(27−9.3+3.2−abc)−3abc =27−3(6−abc)−3abc=27−18=9](https://www.tinkutara.com/question/Q101534.png)
Commented by Rasheed.Sindhi last updated on 03/Jul/20

Commented by 1549442205 last updated on 05/Jul/20
