Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6.-p² - 7q + r

Verified step by step guidance

1. Substitute the given values into the expression: replace \( p \) with \( -4 \), \( q \) with \( 8 \), and \( r \) with \( -10 \).
2. The expression becomes: \(-(-4)^2 - 7(8) + (-10)\).
3. Calculate \((-4)^2\), which is \(16\).
4. Substitute \(16\) back into the expression: \(-16 - 7(8) - 10\).
5. Calculate \(-7(8)\) and then combine all terms to simplify the expression.

Key Concepts

Substitution

Substitution is the process of replacing variables in an expression with their corresponding numerical values. In this question, we substitute p, q, and r with -4, 8, and -10, respectively, to evaluate the expression. This step is crucial for simplifying the expression and obtaining a numerical result.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), this concept is essential for correctly evaluating expressions, especially when they involve multiple operations.

Evaluating Expressions

Evaluating expressions involves calculating the value of an expression after substituting the variables with specific numbers. This process includes performing arithmetic operations as dictated by the order of operations. Understanding how to evaluate expressions is fundamental in algebra and trigonometry, as it allows for the analysis of mathematical relationships.