  In this paper we prove that decomposable forms, or homogeneous polynomials
$F(x_1, \cdots, x_n)$ with integer coefficients which split completely into
linear factors over $\mathbb{C}$, take on infinitely many square-free values
subject to simple necessary conditions and $\operatorname{deg} f \leq 2n + 2$
for all irreducible factors $f$ of $F$. This work generalizes a theorem of
Greaves.
