Question

Plz answer it correctly the best answer will be brainliest.

Answer 1

Answer:

For verifying the given, we need to prove that the left hand side (L.H.S) of the equation is equal to right hand side (R.H.S).

Therefore R.H.S,  

= \frac{1}{2}\left((a+b+c)\left((a-b)^{2}+(b-c)^{2}+(c-a)^{2}\right)\right) \ldots \ldots \ldots=21((a+b+c)((a−b)2+(b−c)2+(c−a)2))………

By using the formula (a-b)^{2}=a^{2}+b^{2}+2 a b(a−b)2=a2+b2+2ab

=21(a+b+c)(a2−2ab+b2)+(b2−2bc+c2)+(c2−2ca+a2)

=\frac{1}{2}(a+b+c) 2\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)=21(a+b+c)2(a2+b2+c2−ab−bc−ca)

=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)=(a+b+c)(a2+b2+c2−ab−bc−ca)

\begin{lgathered}\begin{aligned}=& a^{3}+a b^{2}+a c^{2}-b a^{2}-a b c-c a^{2}+b a^{2}+b^{3}+b c^{2}-a b^{2}-b^{2} c-c a b+c a^{2} \\ &+c b^{2}+c^{3}-a b c-b c^{2}-c^{2} a \end{aligned}\end{lgathered}=a3+ab2+ac2−ba2−abc−ca2+ba2+b3+bc2−ab2−b2c−cab+ca2+cb2+c3−abc−bc2−c2a

After simplification,  

=a^{3}+b^{3}+c^{3}-3 a b c=a3+b3+c3−3abc

L.H.S=R.H.S

Hence, the given equation is proved, that the “left hand side” of the equation is equal to the “right hand side”.