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

Verified step by step guidance

1. Identify the given expression: \(-p^{2} - 7q + r\) and the values \(p = -4\), \(q = 8\), and \(r = -10\).
2. Substitute the values of \(p\), \(q\), and \(r\) into the expression: \(-(-4)^{2} - 7(8) + (-10)\).
3. Calculate the square of \(p\): \((-4)^{2} = 16\).
4. Apply the negative sign in front of \(p^{2}\): \(-16\).
5. Evaluate the entire expression step-by-step: \(-16 - 7 imes 8 - 10\).

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed. Exponents are evaluated before multiplication, addition, or subtraction. For example, in -p², the exponent applies to p before the negative sign is considered, so p² is calculated first, then the negative is applied.

Substitution of Variables

Substitution involves replacing variables with their given numerical values to evaluate an expression. Here, p, q, and r are replaced by -4, 8, and -10 respectively, allowing the expression to be simplified to a numerical value.

Evaluating Algebraic Expressions

Evaluating algebraic expressions means performing arithmetic operations after substituting variables. This includes correctly handling negative signs, exponents, and combining like terms to simplify the expression to a single number.