  We give some new canonical representations for forms over $\cc$. For example,
a general binary quartic form can be written as the square of a quadratic form
plus the fourth power of a linear form. A general cubic form in $(x_1,...,x_n)$
can be written uniquely as a sum of the cubes of linear forms
$\ell_{ij}(x_i,...,x_j)$, $1 \le i \le j \le n$. A general ternary quartic form
is the sum of the square of a quadratic form and three fourth powers of linear
forms. The methods are classical and elementary.
