`(3x-2y+z)^(2)-(3x+2y-z)^(2)`

Write the following in expanded form: (i) (9x+2y+z)^2 (ii) (3x+2y-z)^2 (iii) (x-2y-3z)^2 (iv) (-x+2y+z)^2

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

Simplify: ((x^(2)-y^(2))^(3) + (y^(2) - z^(2))^(3) + (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

Factorize: (3x-2y)^3+(2y-4z)^3+(4z-3x)^3

Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)

Simplify : (x+y+z)^2+(x+y/2+z/3)^2-(x/2+y/3+z/4)^2

Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3

Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3

Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3

Simplify: (x+y-2z)^2-x^2-y^2-3z^2+4x y