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The distributive property is a helpful mathematical tool used to expand expressions that involve both multiplication and addition or subtraction. It allows you to multiply a single term by each term inside a set of parentheses. To understand it better, let's look at the expression in the original exercise: - First, we have the term \(3(x-1)\). - Using the distributive property, you multiply 3 by each term inside the parentheses, resulting in \(3 \times x\) and \(3 \times (-1)\), which simplifies to \(3x - 3\).Next, let's apply the distributive property to another part of the expression:- The term \(4(x+2)\) requires multiplying 4 by each term inside the parentheses.- This gives us \(4 \times x\) and \(4 \times 2\), which simplifies to \(4x + 8\).By applying these calculations, we make the expression more manageable and ready for the next step, which involves combining like terms.

Once you've expanded the expression using the distributive property, the next step is to combine like terms. Like terms in an algebraic expression share the same variable components to the same power.Let's look at the expression we have after distribution: - We have \(3x - 3 + 4x + 8\).- Here, \(3x\) and \(4x\) are like terms because they contain the same variable, \(x\). Adding these gives us \(3x + 4x = 7x\).- Similarly, \(-3\) and \(8\) are the constant terms. Adding these, we get \(-3 + 8 = 5\).By combining like terms, the expression becomes simpler and easier to understand. This process is crucial for simplifying algebraic expressions and finding a more straightforward form.

After using the distributive property and combining like terms, you have a simplified expression. The goal of simplifying is to make the expression as concise as possible while keeping its original meaning.Let's summarize the original problem-solving process:- We started with the expression: \(3(x-1) + 4(x+2)\).- Applied the distributive property to get \(3x - 3 + 4x + 8\).- Combined like terms to simplify it to \(7x + 5\).A simplified expression is easier to handle in further calculations or when solving equations. Simplifying doesn’t always mean solving for a variable; it means making the expression more manageable, elegant, and sometimes more intuitive to interpret.