Math Problem Statement

Evaluate the expression -2(x + 8) - x^2 when x = -4.

Solution

The expression provided in the image seems to be:

2(x+8)x2-2(x + 8) - x^2

We need to evaluate it when x=4x = -4. Let's compute this step by step:

  1. Substitute x=4x = -4 into the expression:

2((4)+8)(4)2-2((-4) + 8) - (-4)^2

  1. Simplify inside the parentheses:

2(4)(4)2-2(4) - (-4)^2

  1. Compute the terms:

2×4=8-2 \times 4 = -8 (4)2=16(-4)^2 = 16

  1. Now subtract:

816=24-8 - 16 = -24

Thus, the expression evaluates to 24-24 when x=4x = -4.

Would you like further details on any part of this solution?

Here are some related questions:

  1. How do you simplify expressions involving negative numbers?
  2. What are the rules for squaring negative numbers?
  3. How do parentheses affect operations in algebraic expressions?
  4. What are common mistakes when simplifying algebraic expressions?
  5. Can you generalize the steps for solving this type of problem?

Tip: When substituting negative values, be careful with signs, especially with powers and parentheses.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Quadratic Expressions

Formulas

Substitution: Replace variable x with a given value.
Exponentiation: x^2 represents x raised to the power of 2.

Theorems

Order of Operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS)

Suitable Grade Level

Grades 7-9