If x,y,z are in A.P., then show that `x^2 + xy + y^2, z^2 +xz + x^2` and `y^2 + yz +z^2` are also in A.P.

Factorise : (x^2 – 2xy + y^2) – z^2

Add: 2x (z – x – y) and 2y (z – y – x)

Factorise 4x^2 + y^2 + z^2 - 4xy - 2yz + 4xz .

If (x+y)/(2),y,(y+z)/(2) are in HP, then x,y, z are in

If x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are also in A.P. then show that x=y=z and y≠0

If z=x+iy and |z+a|=3|z-a|, show that 2(x^2+y^2)=5ax-2a^2 .

If x = 1, y = 3, z = 4, find the value of x^2 + 9y^2 + 4z^2 - 6xy + 12yz -4zx .

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

Factorise the following expressions : x^2 y z + x y^2z + x y z^2