Evaluate each expression for p=-4, q=8, and r=-10. -(p+2)²-3r / 2-q

Verified step by step guidance

1. Substitute the given values into the expression: replace \( p \) with \( -4 \), \( q \) with \( 8 \), and \( r \) with \( -10 \). The expression becomes \(-((-4) + 2)^2 - 3(-10) / 2 - 8\).
2. Simplify the expression inside the parentheses: \((-4) + 2 = -2\).
3. Square the result from the previous step: \((-2)^2 = 4\).
4. Substitute back into the expression: \(-4 - 3(-10) / 2 - 8\).
5. Simplify the expression by performing the multiplication and division: \(-4 + 30 / 2 - 8\).

Key Concepts

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. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions, following this order is crucial to obtaining the correct answer.

Substitution

Substitution involves replacing variables in an expression with their corresponding numerical values. In this question, the variables p, q, and r are substituted with -4, 8, and -10, respectively. This step is essential for simplifying the expression and allows for the evaluation of the mathematical operations involved.

Simplifying Expressions

Simplifying expressions refers to the process of reducing a mathematical expression to its simplest form. This includes combining like terms, performing arithmetic operations, and applying the order of operations. In the context of this question, simplifying the expression after substitution is necessary to arrive at a final numerical value.