Apply the difference of squares identity with decimals: Evaluate (.538^2 − .462^2) / (1 − 0.924) by recognizing algebraic factorization patterns and simplifying cleanly.

Introduction / Context:This question highlights the algebraic identity a^2 − b^2 = (a − b)(a + b). Recognizing this pattern avoids tedious decimal squaring. Pairing that with a straightforward subtraction in the denominator gives a clean simplification to an integer answer.

Given Data / Assumptions:

• Numerator: 0.538^2 − 0.462^2.
• Denominator: 1 − 0.924.

Concept / Approach:Use the identity a^2 − b^2 = (a − b)(a + b). Compute (a − b) and (a + b) once; then multiply. For the denominator, simple subtraction suffices. Compare numerator and denominator to see if cancellation occurs.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• .076: That is the numerator alone, not the final ratio.
• 1.042 or 2: These result from arithmetic or identity misuse.

Common Pitfalls:

• Squaring decimals individually, increasing error risk.
• Forgetting the identity and missing the perfect cancellation.

Final Answer: