Prove that `|{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz`

|(x,1,y+z),(y,1,z+x),(z,1,x+y)|=

Without expanding prove that Delta ={:[( x+y,y+z,z+x) ,( z,x,y),( 1,1,1) ]:} =0

By using properties of determinants , show that : {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

If |(x,y,z),(-x,y,z),(x,-y,z)|=k xyz , then k=

Add the product: x(x+y-r),y(x-y+r),z(x-y-z)

a^(x(y-z))xxa^(y(z-x))xxa^(z(x-y)) =____

Verify that x^3 + y^3 + z^3- 3xyz=1/2 (x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]