91Ó°ÊÓ

When working with algebraic expressions, especially ones that involve multiple operations and parentheses, it's crucial to follow the order of operations. You might have heard of this as PEMDAS or BIDMAS, which stands for parentheses/brackets, exponents/orders, multiplication and division (left to right), and addition and subtraction (left to right). Following this order ensures that mathematical expressions are solved correctly.

In the given expression, \(6 - 5[8 - (2y - 4)]\), we first address the innermost parentheses: \(2y - 4\). The subtraction here must be resolved before moving on to the operations outside of that set of parentheses.

After handling the innermost part, we continue working outward. This requires solving from the brackets outward, making sure each layer is calculated correctly without skipping steps. This systematic method of solving from the inside out is key for maintaining accuracy in your results.

Simplifying expressions means to condense them into a simpler form. This often involves reducing the expression by performing operations within it or combining like terms.

In our example, after solving the operations inside the brackets, the expression \(6 - 5[8 - (2y - 4)]\) changes to \(6 - 5[12 - 2y]\). Here, we achieved simplification by performing operations inside the brackets, including adding or subtracting constants and similar variables. Simplifying frequently means taking small individual steps, like rewriting \(- ( - 2y + 4 )\) to \(+ (2y - 4)\).

Continuing on, we multiply every term inside the bracket by \(-5\), giving us \(6 - 60 + 10y\), thus further simplifying the expression by completing all multiplications. This step involves distributing, which is a common technique in algebra to eliminate parentheses and simplify expressions thoroughly.

Algebraic simplification culminates in reducing an expression to its most concise form. After applying the order of operations and simplifying within the brackets, the final step is to combine like terms.

In our exercise's final expression, \(6 - 60 + 10y\), simplifying involves combining the constant numbers together. Here, \(6\) and \(-60\) are combined to give \(-54\), resulting in \(-54 + 10y\).

The aim of algebraic simplification is to make expressions easier to work with, especially when preparing for further calculations or solving equations. It's about ensuring that no further reductions can be made to create a more straightforward expression, providing clarity and ease for further mathematical operations or insights.