91Ó°ÊÓ

The Distributive Property is a fundamental building block in algebra that helps us to break down expressions, making them simpler to solve. It states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the results. In mathematical terms, it looks like this: \( a(b + c) = ab + ac \). In our original exercise, we apply the distributive property to \(5(x - 2)\). Here, you take the number 5 and multiply it by each term inside the parentheses, which are \(x - 2\). This results in \(5x - 10\). Remember, applying the distributive property correctly can help simplify your expressions and is a key step in algebraic problem-solving.

Simplification in algebra is the process of reducing an expression to its simplest form. This is often achieved by combining like terms, performing arithmetic operations, and applying the distributive property. After applying the distributive property inside the brackets in our exercise, the next step is to simplify the expression \(5x - 10 + 1\). By combining like terms, \(-10 + 1\) simplifies to \(-9\), resulting in \(5x - 9\). Simplification helps make complex expressions more manageable. One tip is always to perform operations step by step, ensuring each transition leads to a clearer and simpler equation.

Removing brackets correctly is crucial in simplifying algebraic expressions. Brackets are used to maintain a certain order of operations, but they must be appropriately managed to achieve a simplified form. In our exercise, after simplifying inside the brackets, we have \(3(5x - 9)\). The brackets here indicate that the 3 should be distributed over \(5x - 9\) using the distributive property. This means that 3 multiplies each term inside, resulting in the simplified form \(15x - 27\). Brackets removal involves careful application of arithmetic operations in the correct order. Always distribute any terms outside the brackets through the terms inside to eliminate them efficiently, leading to the simplest form of the expression.