Evaluate each expression for p=-4, q=8, and r=-10. -p² -7q -r²

Verified step by step guidance

1. Identify the given expression: \(-p^2 - 7q - r^2\) and the values \(p = -4\), \(q = 8\), and \(r = -10\).
2. Substitute the given values into the expression: \(-(-4)^2 - 7(8) - (-10)^2\).
3. Calculate each squared term separately: \((-4)^2\) and \((-10)^2\).
4. Multiply and simplify each term: \(- (p^2)\) becomes \(- (16)\), \(-7q\) becomes \(-7 \times 8\), and \(-r^2\) becomes \(- (100)\).
5. Combine all the simplified terms by performing the addition and subtraction to find the value of the expression.

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed, typically remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This ensures consistent and correct evaluation of expressions, especially when exponents and multiple operations are involved.

Substitution of Variables

Substitution involves replacing variables in an expression with given numerical values. This step is essential to evaluate expressions numerically, allowing the transformation of an algebraic expression into a specific number based on the provided values.

Exponents and Squaring

Exponents indicate repeated multiplication of a base number. Squaring a number means raising it to the power of 2, which affects the sign and magnitude of the result, especially important when dealing with negative values, as squaring a negative number yields a positive result.