`|((x-2)^2,(x-1)^2,x^2),((x-1)^2,x^2,(x+1)^2),(x^2,(x+1)^2,(x+2)^2)|=`

(x-2)^(2),(x-1)^(2),x^(2)(x-1)^(2),x^(2),(x+1)^(2)x^(2),(x+1)^(2),(x+2)^(2)]|=-8

If f(x)=|[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 f(x)=|[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 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 ]]

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

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

The equation |{:((1+x)^(2),(1-x)^(2),-(2+x^(2))),(2x+1,3x,1-5x),(x+1,2x,2-3x):}|+|{:((1+x)^(2),2x+1,x+1),((1-x)^(2),3x,2x),(1-2x,3x-2,2x-3):}|=0

(x^(2))/(x+1)+((x+1)^(2))/(x^(2))-(x)/(x+2)+(x+1)/(x)-(7)/(4)=p^(2)

int((x^(- 6)-64)/(4+2x^(- 1)+x^(- 2))*(x^2)/(4-4x^(- 1)+x^(- 2))-(4x^2(2x+1))/(1-2x))dx