Let's simplify
`x^2 (y^2 - z^3) + y^2(z^2 - x^2) + z^2 (x^2 - y^2)`

Let's simplify:- (x + y) (x^2 -xy + y^2) + ( x - y) (x^2 + xy + y^2)

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

If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|r^2u^2u^2u^2r^2u^2u^2u^2r^2| , where r^2=x^2+y^2+z^2 & u^2= x y + y z+z x

Let us simplify using formula:- (x -y) (x^2 + xy + y^2) + (y - z) (y^2 + yx + z^2) + (z - x) (z^2 + zx + x^2)

Let's find the L.C.M of the following algebraic expressions. x^2 + y^2 - z^2 - 2xy , x^2 - y^2 - z^2 + 2yz, xy + zx + y^2 - z^2

If sin^-1x + sin^-1 y + sin^-1 z = pi , prove that x^4 + y^4 + z^4 + 4x^2y^2z^2 = 2(x^2y^2 + y^2z^2 + z^2x^2)

Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-y)(y-z)(z-x)(x+y+z)(x^2+y^2+z^2)dot

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 : a = y : b = z : c , then prove that (a^(2) + b^(2) + c^(2))(x^(2) + y^(2) + z^(2)) = (ax + by + cz)^(2)

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n (a) x^2+y^2+z^2+x y z=0 (b) x^2+y^2+z^2+2x y z=0 (c) x^2+y^2+z^2+x y z=1 (d) x^2+y^2+z^2+2x y z=1