" 1."(a+b)^(3)-a-b

Show that (1-a)^(3)+(b-1)^(3)+(a-b)^(3)=3(1-a)(b-1)(a-b)

If the points ((a^(3))/(a-1),(a^(2)-3)/(a-1))((b^(3))/(b-1),(b^(2)-3)/(b-1)),((c^(3))/(c-1),(c^(2)-3)/(c-1)) are a!=1,b!=1,c!=1, then find the value of abc-(ab+bc+ca)+3(a+b+c)

The common difference of the AP (1)/(3), (1-3b)/(3), (1-6b)/(3) ,… is

1,1,1a,b,ca^(3),b^(3),c^(3)]|=(a-b)(b-c)(c-a)(a+b+c)

Prove that : log_ea-log_eb=2[(a-b)/(a+b)+1/3((a-b)/(a+b))^3 +1/5((a-b)/(a+b))^5+...],a > b

Prove that : tan^(-1)( (a^3 -b^3)/(1+a^3 b^3)) + tan^(-1)( (b^3 - c^3)/(1+b^3 c^3)) + tan^(-1)( (c^3 - a^3)/(1+c^3 a^3)) = 0