`|[x-1,x^2-x+1],[x+1,x^2+x+1]|=?`

det[[x-1,x^(2)-x+1x+1,x^(2)+x+1]]=?

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

If f(x)=|[1,2(x-1),3(x-1)(x-2)],[x-1,(x-1)(x-2),(x-1)(x-2)(x-3)],[x,x(x-1),x(x-1)(x-2)]| . Then, the value of f(2020) 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

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 us simplify using formula:- (x+1) (x^2 - x + 1) + (2x - 1) (4x^2 + 2x + 1) - (x-1)(x^2 + x + 1)

Value of |1+x_1 1+x_1x1+x_1x^2 1+x_2 1+x_2x1+x_2x^2 1+x_3 1+x_3x1+x_3x^2| depends upon "xo n l y" b. "x"_1"o n l y" c. "x"_2on l y d. none of these

Value of |1+x_1 1+x_1x1+x_1x^2 1+x_2 1+x_2x1+x_2x^2 1+x_3 1+x_3x1+x_3x^2| depends upon "xo n l y" b. "x"_1"o n l y" c. "x"_2on l y d. none of these

|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3