
Homogeneous Expression: If all the terms of an algebraic expression are of the same degree, then such an expression is called homogeneous expression We denote the coefficients by a, b, c, d, ...etc. and the variables x, y, z.
Example:

Variables  Degree  Standard Form 

x, y  1  ax + by 
x, y  2  ax^{2} + bxy + cy^{2} 
x, y  3  ax^{3} + bx^{2}y + cxy^{2} + dy^{3} 
. . . . .  . . . . .  . . . . . 
x, y, z  1  ax + by + cz 
x, y, z  2  ax^{2} + by^{2} + cz^{2} + dxy + eyz + fzx 
x, y, z  3  ax^{3} + by^{3} + cz^{3} + dx^{2}y + exy^{2} + fy^{2}z + gyz^{2} + hz^{2}x + kzx^{2} + lxyz 