91Ó°ÊÓ

The distributive property is a fundamental concept in algebra that allows us to simplify expressions. It states that multiplication distributed over addition or subtraction inside parentheses means multiplying every term inside the parentheses. In the expression ewlineewline3-2[5(x-10y)-(3+2y)], the first step involves distributing the multiplication: 5(x - 10y) and -(3 + 2y). Using the distributive property, we get: 5x - 50y and - 3 - 2y. Now, the expression becomes: 3 - 2[5x - 50y - 3 - 2y]. This property helps break down complex expressions into simpler parts, making it easier to solve.

Combining like terms is essential in simplifying algebraic expressions. Like terms are terms that have the same variables raised to the same power. In our example, inside the brackets 5x - 50y - 3 - 2y let's identify and combine like terms. The terms -50y and -2y are like terms because they both contain the variable y. Combining them gives us -52y. So the expression simplifies to: 3 - 2(5x - 52y - 3). By grouping and combining like terms, we reduce the number of terms and simplify the expression further. This step is crucial for reaching the final simplified form.

Parentheses in algebra indicate that the terms inside need to be handled as a single unit first. They often signify the need to apply the distributive property or to simplify within them before performing other operations. In our problem, the expression within the parentheses, 5(x-10y)-(3+2y), needs to be simplified before we can subtract or add it from/to other terms. After distributing and combining like terms inside the parentheses, we deal with the expression 3 - 2(5x - 52y - 3). Next, we distribute the -2 to each term inside the parentheses, giving us: -10x + 104y + 6 . Finally, when we add the remaining terms outside the parentheses, 3 + 6, the entire expression simplifies to -10x + 104y + 9. Handling parentheses correctly is key to simplifying and solving algebraic expressions accurately.