In $a - (a + 2)=-2$, how did the $2$ become $-2$? I'm new to math. I would like to ask for you help to explain solving the following:
$$a - (a + 2)= -2$$
I didn't understand how the $2$ became $-2$.
Is there a good reference to learn these step by step?
Thanks
 A: The minus is distributive, like multiplying the amount in parentheses by $(-1).\space$ Expanding, we get.
$a-(a+2)=a-a-2\quad =0-2=-2$
A: Perhaps think of '$a$' as some other number like $5$.
$$5-(5+2)=-2$$
$$5-(7)=-2$$
$$-2=-2$$
Or think of using $10$ in place of '$a$'
$$10-(10+2)=-2$$
$$10-(12)=-2$$
$$-2=-2$$
In fact it does not matter what number is used in place of '$a$' the statement given is always true: if you subtract 'some number' minus 'two more than that number' you will get two less than you start with.
A: I give you $a$ sweets
I give your brother $b$ sweets.
How much more sweets do you have compared to your brother? Well, $a-b$.
Now you found out that your brother has $a+2$ sweets. Well, it is $a-(a+2)$.  You actually have $2$ sweets less than your brother, not more. So $a-(a+2)=-2$.
By distributive law, we have $c(d+e)=cd+ce$.
$$-(a+2)=-a-2$$
Hence $$a-(a+2)= a+ (-1)(a+2)=a+(-a-2) = (a-a) -2=-2$$
where we use distributive law in the second equation  and associativity of addition in the next equation.
