91Ó°ÊÓ

Distribution is a key skill in algebra that helps to simplify expressions by spreading out terms, particularly when there are parentheses involved.
This process follows the **distributive property** which states that:
\[ a(b + c) = ab + ac \]
In the context of the exercise, the distribution happens in Step 1 when we distribute the negative sign before the parentheses.
The original expression is:
\[ 2t - 5 - (3t - 6) \]
Here, the negative sign in front of the parentheses changes the signs of the terms inside. So, we follow the rule:
\[ - (3t - 6) = -3t + 6 \]
Finally, substituting back, the expression simplifies to:
\[ 2t - 5 - 3t + 6 \]

After distribution, the next step is combining like terms to further simplify the expression.
**Like Terms** are terms that have the same variables raised to the same power. Only their coefficients differ.
For example, in the expression:
\[ 2t - 5 - 3t + 6 \]
Notice the terms involving 't': 2t and -3t. These are like terms. Similarly, -5 and 6 are constant like terms.
Group and combine them:
\[ (2t - 3t) + (-5 + 6) \]
Simplifying each group:
\[ 2t - 3t = -t \]
and
\[ -5 + 6 = 1 \]
Putting these simplified terms together, the expression is:
\[ -t + 1 \]

Handling negative signs is crucial when simplifying algebraic expressions. Mismanagement can lead to errors.
In algebra, a negative sign can change the value and orientation of terms.
For example, the negative sign in front of (3t - 6) in the expression \[ 2t - 5 - (3t - 6) \] distributes to the terms inside giving:
\[ -3t + 6 \]
This changes both the terms inside the parenthesis.
Always be careful when distributing negative signs. Treat them consistently as multiplying by -1.
Ignore parentheses first, then attach a minus to each internal term:
\[- (3t - 6) = -3t + 6 \]
In Step 2, the gathered terms with negative signs, like -3t and -t, were carefully managed to ensure proper addition and subtraction.