Using properties of determinant show that : `|(-x^2,xy,xz),(xy,-y^2,yz),(xz,yz,-z^2)|=4x^2y^2z^2`

Using properties of determinant show that : |((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

Using properties of determinant show that : |(y+z,x,x),(y,z+x,y),(z,z,x+y)|=4xyz

Factorise : |(1,1,1),(x,y,z),(x^2,y^2,z^2)|

Show that |(x, x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y)| = (y-z)(z-x)(x-y)(x+y+z) .

if y = sin^-1x , show that (1-x^2) y_2 = xy_1

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

Prove that (x+2y+3z)^3-x^3-8y^3-27z^3=3(2y+3z)(x+3z)(x+2y)

Resolve into factors y^2(2x-z)+z^2(2x-y)-4x^2(y+z)+6xyz

Resolve into factors x(y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)

Prove that (3x-2y)^3+(y-2z)^3+(y+2z-3x)^3=3(3x-2y)(y-2z)(y+2z-3x)