" ve that "|[1,x,x^(2)],[x^(2),1,x],[x,x^(2),1]|=(1-x^(3))^(2)

Prove that |(1,x,x^2),(x^2,1,x),(x,x^2,1)|=(1-x^2) .

By using properties of determinants , show that : {:[( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) ]:} =( 1-x^(3)) ^(2)

[[3x^(2),3x,1x^(2)+2x,2x+1,12x+1,x+2,1]]=(x-1)^(3)

If f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]

If D(x)=det[[x-1,(x-1)^(2),x^(3)x-1,x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3)]] then

prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1))|=6x^(2)(1-x^(2))

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

Let f(x)=|(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x)| then |f(2.9)^(1//3)|= ___________

(1-2x+x^(2))/(1-x^(3))times(1+x+x^(2))/(1+x)