How do you distribute this negative?

Question

So I have $-(x - 2)^2$. Do I rewrite it as $-(x - 2)\cdot-(x - 2)$ and distribute the negative to the inside making it $(-x + 2)(-x + 2)$ or add the negative at the end of doing FOIL?

Answer 1

$$-(x-2)^2=-(x-2)\cdot (x-2)=-(x^2-4x+4)$$

Answer 2

The minus sign is not in the scope of the exponent, so apply the minus AFTER squaring what's in parentheses.

To indicate the other, you would have to write $(-(x-2))^2$.

In the absence of inclusion symbols such as parentheses, brackets, braces, etc., exponents only apply to the immediately preceding factor that carries them.

Answer 3

Just square $(x-2)$ and negate it, i.e. multiply it by $-1$

Answer 4

$-a^2$ interpreted as $-(a^2)=-(a\cdot a)$. The reason is that, in the order of operations, exponentiation comes before subtraction. Thus, $-3^2=-9$, and $-(x-2)^2=-(x-2)(x-2)$.