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Understanding how to substitute values into algebraic expressions is a fundamental skill in algebra. This process involves replacing the variables in an expression with their corresponding numerical values. For instance, let's say we have variables such as a, b, c, and d with assigned values. When an expression contains these variables, we directly substitute the values in their place.

To do this effectively, you should align the variables and their values to avoid any confusion. For our example of evaluating the expression d(b+a), we first identify the values of a=3, b=-2, and d=2. We then replace a with 3 and b with -2 in the expression, leading to an updated version that is ready for further simplification: 2(-2 + 3). Remember, the substitution is just the beginning; it sets the stage for applying the correct order of operations to simplify the expression.

To accurately evaluate expressions, one must follow the order of operations, commonly remembered by the acronym BIDMAS or PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). This rule is vital to ensure consistency in simplifying algebraic expressions.

Following the order, we first handle operations inside parentheses. In our expression 2(-2 + 3), addition within the parentheses is done first, resulting in 2(1). We then proceed to multiplication as no exponents are present. Division and multiplication are handled before addition and subtraction and carried out from left to right. By obeying this strict sequence, we avoid mishaps that can occur when operations are performed out of order.

To simplify the expression further, we multiply the remaining terms following the order of operations. After the substitution and dealing with the parentheses, we now have 2(1). The final step in our basic example is simply to multiply 2 by 1.

This step is straightforward, yet it is a fundamental aspect of simplifying algebraic expressions. Simplification aims to reduce expressions to their simplest form by carrying out all possible operations. In more complex scenarios, this might involve combining like terms, factoring expressions, or using algebraic identities. However, for our example, multiplication yields the final simplified result: 2.

Remember, simplification not only makes expressions easier to work with but also helps in better understanding the relationship between mathematical symbols and the numbers they represent.