Factorise a^3 + b^3 + c^3 - 3abc

Factorize a^3 + b^3 + c^3 - 3abc

Related Topics :-
a^3 + b^3 + c^3 - 3abc
a^3+b^3+c^3 formula
a^3+b^3+c^3 formula proof
factoring
special identities a^3 + b^3 + c^3 - 3abc
a^3 + b^3 + c^3 - 3abc =
a^3 + b^3 + c^3 - 3abc explained

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[raghvendrasingh]

Another proof without using sum of cubes formula
a^3 = (a^2) (p-b-c) where p = a+b+c
or a^3 = pa^2 - a ( ab+ ca)
similarly for b^3 and c^3
hence given expression is
p( a^2+b^2+c^2) -a (ab+ca) - b (bc+ab) - c(ca+bc) - abc - abc - abc
= p (a^2+b^2+c^2) - a(ab+bc+ca) - b( ab+bc+ca ) - c ( ab+bc+ca )
= (a+b+c)(a^2+b^2+c^2) - (a+b+c) (ab+bc+ca)
= (a+b+c) (a^2+b^2+c^2 - ab-bc-ca)

[honestadministrator]

( a + b) ^3 + c^3 -3 ab ( a + b) -3 a b c
= (a + b + c)
( a^2 + b^2 + 2 a b - c ( a + b).+ c^2
- 3 a b)
= (a + b + c)
(a^2 +b^2 +c^2 - a b - c a - b c)
- 3 a b)

[manavdangwal]

Pls can you make videos on trigonometry. ❤