Prove that `|axxb^2 =a^2b^2 - (a.b)^2`

Prove that |axxb|^2 =a^2b^2 - (a.b)^2

Prove that |axxb|^2 =a^2b^2 - (a.b)^2

Prove that |axxb|^2=a^2b^2-(a*b)^2 .

If vec a and vec b are two vectors,then prove that (vec a xxvec b)^(2)=a^(2)b^(2)-(a.b)^(2)

Prove that: (a-b)^(2)=a^(2)-2ab+b^(2)

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2

Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2 .

Prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

Using properties of determinant : Prove that |(a^(2), 2ab, b^(2)),(b^(2),a^(2),2ab),(2ab,b^(2),a^(2))| = (a^(3) + b^(3))^(2)