[tex]-a^2=(-1)\cdot a\cdot a[/tex]
Regardless of the sign of [tex]a[/tex], we have [tex]a\cdot a=a^2\ge0[/tex] (never negative). But multiplying by -1 makes it negative.
On the other hand,
[tex](-a)^2=((-1)\cdot a)^2=(-1)^2\cdot a^2=1\cdot a^2=a^2[/tex]
which can never be negative for real [tex]a[/tex].
