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Algebra often deals with simplifying expressions to make them easier to work with and understand. This practice involves transforming expressions into simpler forms without changing their value. To simplify an expression, it's essential to first interpret and break it down into manageable parts, as seen in the exercise:\[-(t - 2u) + (3u - t)\]The goal is to rewrite this expression in a way that's most straightforward, consisting of fewer terms or combinations of like terms. This process involves carefully applying algebraic rules, such as the distributive property and combining like terms, to achieve a simplified outcome.

Distributing negative signs is a crucial step in simplifying algebraic expressions. When you encounter a negative sign outside of parentheses, it means you have to distribute it to each term inside. This involves changing the signs of each of those terms:In the expression:\[-(t - 2u)\]We distribute the negative sign by changing the sign of each term inside the parentheses:\[-t + 2u\]This approach ensures that the negative sign affects both the "\(t\)" and the "\(2u\)" inside the brackets. As a result, this becomes:\[-t + 2u + 3u - t\]This method removes the parentheses, allowing you to combine any like terms easily.

The process of combining like terms is an essential part of simplifying algebraic expressions. Like terms are terms that have the same variable and can be combined by adding or subtracting their coefficients. For example:- In the expression: - \(-t + 2u + 3u - t\)You identify like terms:- The terms \(-t\) and \(-t\) can be combined. Since both terms have the same variable "\(t\)", they add up to: - \(-2t\)- Similarly, the terms with the variable "\(u\)" are \(2u\) and \(3u\). These can be combined to result in: - \(5u\)So, the simplified form of the expression becomes:\(-2t + 5u\)By combining terms in this manner, algebraic expressions are streamlined into simple forms that are easier to analyze and solve for values of variables.