why is -3 squared = - 9 but (-3) squared =9

Question

What do parenthesis do to a negative integer compared to an integer with out parenthesis?

Answer 1

An exponent governs only the symbol upon which it sits:

-3², the exponent sits on the 3 and only the 3 is squared, -9

(-3)², the exponent sits on the parenthesis so everything inside is squared, 9

Answer 2

A 3 is considered positive.  That is, the "+" is optional.

 

A -3 is negative.  This is called a "unary minus";  it means the same as 0-3.

 

A 3² is positive (note: the "+ is optional).

 

A -3² is the same as -9 because P-E-M-D-A-S requires the Exponentiation to be performed before the unary minus (which is the same as Subtraction [that is, 0-9].

 

So:  -3²  =  -(0+3)²  = -9    [this means "0-9"]  [note: this is called a "binary minus"]

       (-3)² = +9             [remember the "+" is optional and means "0+9"]

Answer 3

In the first case, -3², the order of operations rules dictate that the squaring has 'priority' over the leading -; the 3 squared gives9, and then the lower priority leading sign gives the opposite of that 9.

 

In the latter case, the quantity in parentheses, -3, is to be multiplied by itself: (-3)(-3) gives 9 because a negative times a negative is a positive.

 

 

Answer 4

3² equals +9, as (+3) times (+3) = +9

(-3) squared also equals +9, as a negative number, times another negative number, is positive. So, (-3) x (-3) = +9

But, as 3² = 9, then the negative of this will be negative 9, i.e. -(3²)= -9