`(-a^2+c^2)(c^2+a^2)`

Simplify the (a^2+b^2)(a^2-b^2)+(b^2+c^2)(b^2-c^2)+(c^2+a^2)(c^2-a^2)

Resolve into factors a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) + 2abc

Resolve into factors a^2b^2(a^2-b^2)+b^2c^2(b^2-c^2)+c^2a^2(c^2-a^2)

If a + b + c = 0 , then prove that (2a^2)/(a^2-b^2-c^2)+(2b^2)/(b^2-c^2-a^2)+(2c^2)/(c^2-a^2-b^2)=3

If a,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2) are in GP.

If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) are in G.P. (a^2-b^2),(b^2-c^2),(c^2-d^2) are in G.P. 1/(a^2+b^2),1/(b^2+c^2),1/(c^2+d^2) are in G.P.

Factorise : b^(2)c^(2)(b^(2)-c^(2))+c^(2)a^(2)(c^(2)-a^(2))+a^(2)b^(2)(a^(2)-b^(2))

What is the value of (a^2+ac)/(a^2c-c^3)-(a^2-c^2)/(a^2c+2ac^2+c^3)-(2c)/(a^2-c^2)+3/(a+c)