Why is -a squared in brackets different from -a squared?

Answer 1

-a2 differs from (-a)2 because the brackets change the order in which operations are done. Normally, exponents are handled before addition, subtraction, multiplication and division. This means that in the first expression, -a2, we are subtracting the square of the value a. In other words, our first expression could also be expressed as -(a × a). Brackets however are used to specify a set of operations that need to be done first. This means that our second expression would instead be broken down as (-a) × (-a).

The resulting difference between the two is that the first expression will always give us a negative number, and the second one will always give us a positive number (assuming imaginary numbers are not involved).