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 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

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

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

Factorise 4x ^(2) + 9y ^(2) + 25 z ^(2) - 12 xy - 30 yz + 20 zx

Simplify the following: -x+y+z-(2x-3y+z)

By using properties of determinants , show that : {:|( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) |:} =( x-y)(y-z) (z-x) (xy+yz+ zx)

The three adjacent surfaces of cuboid are x sq. unit, y sq. unit and z sq. unit. The length of its one of the diagonal is Option 1 (xy/z+yz/x+zx/y)^(1/2) Option 2 ( z x/ y + x y/ z + y z/ x )^(1/2) Option 3 ( x y/ z + y z/ x + z x/ y ) Option 4 ( z y/ x + y z/ x + x y/ z )

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

Let's find the product by successive multiplication____ (frac(x^2)(y^2) + frac(y^2)(z^2)), (frac(y^2)(z^2) + frac(z^2)(x^2)), (frac(z^2)(x^2) + frac(x^2)(y^2))