Verify : `x^3 + y^3 = (x + y) (x^2- xy + y^2)`

Verify (i) x ^(3) + y ^(3) = (x + y) (x ^(2) -xy + y ^(2)) (ii) x ^(3) -y ^(3) = (x-y) (x ^(2) +xy +y ^(2)) using some non-zone positive integers and check by actual multiplication. Can you call these as identities ?

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

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

(3x - 2y)^2 - (3x - 2y)^2 = ___

If A = 5x^2 + 3xy + 2y^2 , B = - 2y^2 - 3xy + 4x^2 then A + B __

If x^2 + xy + 3y^2 = 1 then (x + 6y)^3 (d^2y)/(dx^2) is

The coefficient of x^3 in (2x-3y) (4x^2+6xy+9y^2) is

Factorise 8x ^(3) + 36 x ^(2) y + 54 xy ^(2) + 27 y ^(3).