`(a^2+b^2+2ab)-(a^2+b^2-2ab)`

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):}|

If a =0, b =3, find the value of frac(a^2+2ab+b^2)(a^2 -2ab + b^2)

Find the compounded ratio of: (a-b): (a+b) and (b^(2) + ab): (a^(2) -ab)

a^3 - b^3 - 3a^2b+ 3ab^2, by, a^2 + b^2 - 2ab

Simplify (a - b) (a ^(2) + b ^(2) + ab) - (a +b) (a ^(2) +b ^(2) - ab)

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

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

Using properties of determinants prove that |(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),2ab,a^(2))|=-(a^(3)+b^(3))^(2) .

If a and b are real and i=sqrt(-1) then sin[i ln((a+ib)/(a-ib))] is equal to 1) (2ab)/(a^(2)-b^(2)) 2) (-2ab)/(a^(2)-b^(2)) 3) (2ab)/(a^(2)+b^(2)) 4) (-2ab)/(a^(2)+b^(2))