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In algebra, the distributive property is a guideline to simplify expressions and equations. It states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. For instance, in the given exercise, we see the expression: \(4t - 2(t - 3)\).

We need to distribute the \(-2\) across the terms inside the parentheses. Doing this correctly means multiplying \(-2\) by both \(t\) and \( -3\). This results in: \(4t - 2t + 6\).
Remember, always pay attention to the sign that you distribute! It is crucial to understanding and correctly applying the distributive property. It helps make otherwise complicated expressions simpler.

Combining like terms is another fundamental concept in algebra for simplifying expressions. Like terms are terms in an expression that have the same variable raised to the same power. In our simplified expression from the first step, we get: \(4t - 2t + 6\).

Here, \(4t\) and \(-2t\) are like terms because they both contain the variable \(t\). Combining them is straightforward: \(4t - 2t = 2t\). Now, our simplified expression looks like this: \(2t + 6\).
This step is vital because it helps to reduce the expression to its simplest form.

Understanding expressions in algebra is key to solving problems effectively. An expression is a combination of numbers, variables, and operations (such as addition or multiplication) grouped together.

Our initial expression was \(4t - 2(t - 3)\). It's a bit complex due to the parentheses and different terms. Simplifying it involves using both the distributive property and combining like terms, as we've seen. The goal is always to break down the expression into a simpler, more manageable form.

Once simplified to \(2t + 6\), the expression is much easier to work with and understand. Working step-by-step and systematically applying these concepts helps to demystify algebraic expressions!