Question

slove it by step by step​

Answer 1

Step-by-step explanation:

$\pmb{ \red{\[ \begin{aligned} & \tt \text { (i) Consider, L.H.S }=(a b+b c)(a b-b c) \\ & \tt+(b c+c a)(b c-c a)+(c a+a b)(c a-a b) \\ -& \tt a b(a b-b c)+b c(a b-b c)+b c(b c-c a) \\ & \tt+c a(b c-c a)+c a(c a-a b)+a b(c a-a b) \\ \\ =& \tt a^{2} b^{2}-a b^{2} c+a b^{2} c-b^{2} c^{2}+b^{2} c^{2}-b c^{2} a+\\ & \tt a b c^{2}-c^{2} a^{2}+c^{2} a^{2}-c a^{2} b+a^{2} b c-a^{2} b^{2} \\ \\ =& 0=\text { R.H.S. } \end{aligned} \]}}$

$\pmb{\orange{\[ \begin{array}{l} \tt(ii) \: \: \: \text { Consider, L.H.S. }=(a+b+c)\left(a^{2}+b^{2}+c^{2}\right. -a b-b c-c a) \\ \\ \tt =a\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)+b\left(a^{2}+b^{2}+c^{2}\right. \\ \tt -a b-b c-c a)+c\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right) \\ \\ \tt =a^{3}+a b^{2}+a c^{2}-a^{2} b-a b c-c a^{2}+b a^{2}+b^{3} \\ \tt +b c^{2}-a b^{2}-b^{2} c-a b c+c a^{2}+c b^{2}+c^{3}-a b c -b c^{2}-c^{2} a\\ \\ \tt =a^{3}+b^{3}+c^{3}-3 a b c=\text { R.H.S } \end{array} \]}}$