Let's write the value of `x^3 - y^3 -z^3 - 3xyz` if x = y + z

Let's write the value of x^3 + y^3 by calculations if x + y = 2 and frac(1)(x) + frac(1)(y) = 2

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

If x = y = 222 and z = 223, then find the value of x^(3)+y^(3)+z^(3)-3xyz

Let's find value of : (x - y)a + (y - z) b + (z -x)c if a = x^2 + xy + y^2,b = y^2 + yz + z^2, c = z^2 + zx + x^2

x^(3)-8(y-z)^(3)

Let's find the product by formulas: (2x - y + 3z) (2x + y + 3z)

If x,y,z, are real and distinct number, then the value of ((x-y)^3+(y-z)^3+(z-x)^2)/((x-y)(y-z)(z-y)) is

If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a. 1 b. 2 c. -1 d. 2

Find the values of x ,\ y,\ z if the matrix A=[(0,2y,z), (x, y,-z ),(x,-y, z)] satisfy the equation A^T\ A=I_3 .

x^(3)+8y^(3)+27z^(3)-18xyz