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

prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the value of the following determinant : |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|

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

Prove that, abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)) =4 a^2b^2c^2 .

Prove that, |{:((b+c)^(2),c^(2),b^(2)),(c^(2),(c+a)^(2),a^(2)),(b^(2),a^(2),(a+b)^(2)):}|=2(bc+ca+ab)^(3)

Prove that, abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)) =1+ a^2+b^2+c^2 .

prove that, |{:(""-bc ,b^2+bc,c^2+bc),(a^2+ac," "-ac,c^2+ac),(a^2+ab,b^2+ab," "-ab):}|=(ab+bc+ca)^3

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Show that: abs(((b+c)^2,a^2,bc) , ((c+a)^2,b^2,ca) , ((a+b)^2,c^2,ab))=(a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)

Prove that {:|( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) |:} =4a^(2) b^(2) c^(2)

Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c^2 .