sammichelle21 sammichelle21
  • 04-05-2018
  • Mathematics
contestada

why is -a² is always negative (a ≠ 0) and why is (-a)² is always positive?

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LammettHash
LammettHash LammettHash
  • 04-05-2018
[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].
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