Question

If \(a = -2\) and \(b = 5\), then \(a^2 + b^2\) =

• A. -29
• B. -21
• C. 3
• D. 21
• E. 29

Hint:

Be extremely careful when squaring negative numbers. Always enclose the negative number in parentheses. \( (-2)^2 = 4\), but \(-2^2 = -4\). The parentheses make all the difference.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This problem requires substituting given values for variables into an algebraic expression and then evaluating it using the correct order of operations.
Step 2: Key Formula or Approach:
Substitute \(a = -2\) and \(b = 5\) into the expression \(a^2 + b^2\).
Step 3: Detailed Explanation:
The expression is \(a^2 + b^2\).
Substitute the given values:
\[ (-2)^2 + (5)^2 \] First, evaluate the exponents. It is crucial to use parentheses when squaring the negative number.
\[ (-2)^2 = (-2) \times (-2) = 4 \] \[ (5)^2 = 5 \times 5 = 25 \] Now, add the results:
\[ 4 + 25 = 29 \] Step 4: Final Answer:
The value of the expression is 29. This corresponds to option (E).