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The distributive property is a fundamental algebraic principle. It allows you to simplify expressions and solve equations more easily. When you apply the distributive property, you multiply a single term by each term within a set of parentheses. In our example, we started with \(3x(x-2)\). - First, we distribute \(3x\) to \(x\) inside the parentheses, resulting in \(3x * x\). - Next, distribute \(3x\) to \(-2\), giving us \(3x * -2\). This step's purpose is to "distribute" the multiplication over each term in the parentheses, so nothing is left combined under the parentheses. It's like passing out cookies to each child in a group—all need to get some! Mastering this skill will help you handle complex equations systematically.

Algebraic expressions are combinations of numbers, variables, and operations. They form the basis of many mathematical problems. In this exercise, the expression \(3x(x-2)\) includes a coefficient (3), a variable (\(x\)), and terms inside parentheses - The coefficients are the numerical parts attached to the variables and indicate how much of that variable you have. - The terms inside the parentheses are \(x\) and \(-2\), which need to be interacted with the initial \(3x\). Understanding these components is essential. They set the stage for tasks like simplification, solving equations, and performing polynomial operations. Remember that variables like \(x\) can change value, enhancing the versatility of algebraic expressions in representing real-world situations.

Simplification refers to the process of rewriting an expression in its simplest form. It's like tidying up a room; you're making the expression more straightforward to work with. For the expression \(3x(x-2)\), after applying the distributive property, we simplify further:- We multiply \(3x * x\) to get \(3x^2\). - Then, we multiply \(3x * -2\) to obtain \(-6x\). So, the expression simplifies from \(3x(x-2)\) to \(3x^2 - 6x\). This final expression has no like terms to combine and represents the original problem in a tidier format. It helps you understand the expression's structure better when it's in this simplified form, making it easier to solve related equations or perform further operations on it.