Simplify the expression using the difference of squares: [ (999 + 588)^2 − (999 − 588)^2 ] / (999 * 588 ).

Introduction / Context:
Expressions of the form A^2 − B^2 invite the identity A^2 − B^2 = (A − B)(A + B). Recognizing this turns intimidating large numbers into small, easily cancelable factors—perfect for mental math under time pressure.

Given Data / Assumptions:

• A = 999 + 588, B = 999 − 588.
• Compute [A^2 − B^2] / (999 * 588).

Concept / Approach:
Use the difference-of-squares identity to factor the numerator. Then simplify the fraction by canceling common factors with the denominator. Because A + B and A − B become simple combinations of 999 and 588, the cancellation is straightforward.

Step-by-Step Solution:
A − B = (999 + 588) − (999 − 588) = 1176.A + B = (999 + 588) + (999 − 588) = 1998 = 2 * 999.Numerator = (A − B)(A + B) = 1176 * 1998 = 1176 * (2 * 999).Divide by denominator 999 * 588: cancellation of 999 gives 1176 * 2 / 588 = 2352 / 588 = 4.

Verification / Alternative check:
Compute 2352/588 by noticing 588 * 4 = 2352 — exact equality confirms the result.

Why Other Options Are Wrong:

• 8, 3, 2, 6: These stem from partial cancellations or miscomputing A + B.

Common Pitfalls:
Forgetting that A + B = 2*999; arithmetic errors in 1176 or in the final division.

Final Answer:
4