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)

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)

Find the value of (yz)^(log y - log z) xx (zx)^(log z - log x) xx (xy)^(log x - log y) .

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

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

Find square root of x + y + z + 2 sqrt(yz) + 2sqrt(zx) + 2sqrt(xy)

If x^2+y^2+z^2=1 , then xy + yz + zx lies in

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 )

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