36.4k views
5 votes
Why is -a² is always negative (a ≠ 0) and why is (-a)² is always positive?

1 Answer

7 votes

-a^2=(-1)\cdot a\cdot a

Regardless of the sign of
a, we have
a\cdot a=a^2\ge0 (never negative). But multiplying by -1 makes it negative.

On the other hand,


(-a)^2=((-1)\cdot a)^2=(-1)^2\cdot a^2=1\cdot a^2=a^2

which can never be negative for real
a.
User Karim Taha
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.