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Variable substitution is like swapping out placeholders in an expression with actual numbers. Imagine you have an equation that needs fine-tuning to speak directly about the situation you face. In the exercise, we are given the expression \(x^2 - y\), and we need to evaluate it using specific numbers for \(x\) and \(y\).
We replace \(x\) with -2 and \(y\) with 4. This step transforms the expression into its numerical form: \((-2)^2 - 4\).
This replacement is crucial in mathematics because it allows you to calculate an expression based on real-world data or specific scenarios. It's like putting fuel into an engine to see how far it can go. You'll use the new numbers in place of the variables to move on to the next step, expression evaluation.

Expression evaluation involves performing the operations indicated in the expression, using the numbers from the substitution. It means working through the math to arrive at a final value.
Once we substitute \(x = -2\) and \(y = 4\) into the expression \(x^2 - y\), it becomes \((-2)^2 - 4\).

• The first task is to calculate \((-2)^2\), which results in 4. Squaring a number means multiplying it by itself, so in this case, \((-2) \times (-2) = 4\).
• Next, subtract the substituted value of \(y\), which is 4, from the squared result. Thus, \(4 - 4\) equals 0.

Just like fitting pieces together in a puzzle, each step depends on finishing the previous one before moving forward. After completing the steps in order, we discover the evaluated value of the original expression.

The order of operations is the sequence of steps to follow when solving an expression. Think of it as rules for a game or instructions for assembling furniture. It tells you how to proceed when multiple operations appear in an expression.
We use the acronym PEMDAS to remember this order:

• Parentheses first
• Exponents (like powers or roots)
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)

In our given expression \(x^2 - y\), after substituting the variables, we handle the exponent first because it's higher in the order than subtraction. We calculate \((-2)^2\) before performing the subtraction of 4.
Following this order ensures accurate results. Skipping steps or mixing them up could lead to incorrect answers. By respecting this hierarchy, we can correctly evaluate and understand expressions every time. It's like having a roadmap for unfamiliar terrain.