negative number squared

Think about this

what is   $$17-3^2 \;\;\;?$$

Well I expect that you would agree it is 17-9 = 8

so..... $$-3^2=-9$$      How can this be justified?

 

WELL

$$(-3)^2=-3*-3=+9$$

BUT

$$-3^2=-1*3^2=-1*3*3=-9$$

 

So there is an invisable   1*    between the minus sign and the 3.

That is how it can be justified!

 

So to summerize

$$\\-3^2=-9\\
(-3)^2=+9$$