Golden Rule:
Distributing a negative sign flips the sign of every term inside the parentheses (bracket).
Positive becomes negative, and negative becomes positive.
Let's take \(a\) and \(b\) as two integers and apply the golden rule.
\(- (a + b) = - a - b\)
\(- (-a + b) = a - b\)
\(- (a - b) = -a + b\)
\(- (-a - b) = a + b\)
Example:
Find the value of \(- (2 + 3) - (-5 - 1)\).
Solution:
Given expression is \(- (2 + 3) - (-5 - 1)\).
Let us first distribute negative signs inside the bracket.
So, positive becomes negative and negative becomes positive.
\(- (2 + 3) - (-5 - 1)\) \(=\) \(- 2 - 3 + 5 + 1\)
\(=\) \(- 5 + 5 + 1\)
\(=\) \(1\)
Thus, the value of the given expression is \(1\).