Adding/subtracting negatives

Question

Explain why -(a - b) = b-a

Answer 1

-(a-b)

distribute the coefficient of the parenthetical expression among the terms inside the parentheses

there's an implicit -1 as the coefficient

-1 times a plus -1 times -b

the distributive property of multiplication

= -1(a) + (-1)(-b)

= -a +b

switch the order, the order doesn't matter

the commutative property of addition

= +b -a

= b -a