Question

what is the difference among a^2, -a^2, (-a)^2,
-(a^2)?

Answer 1

a^2 = (-a)^2
-a^2 = -(a^2)

Answer 2

\[a ^{2} = a*a\]
\[-a ^{2} = -(a*a)\]
\[(-a)^{2}=(-a)*(-a)\]

The middle one would always give you a negative number, whereas the other two would always give you a positive number.

Answer 3

a^2 = a^2
-a^2 = -1 x a^2
(-a)^2 = a^2
-(a^2) = -a^2

Answer 4

Oops. Forgot the last one. It would essentially be the same as the middle one in my last reply.