Evaluate the expression [(798 + 579)^2 - (798 - 579)^2] divided by (798 × 579) and choose the correct value.

Introduction / Context:

This question tests your ability to recognize and use the algebraic identity for the difference of squares. Rather than expanding the large squares directly, you save time by applying a standard formula, which is a key skill in quantitative exams.

Given Data / Assumptions:

• The expression is [(798 + 579)^2 - (798 - 579)^2] / (798 × 579).
• We need to find the exact numerical value.
• All arithmetic is done with real numbers.

Concept / Approach:

Use the identity A^2 - B^2 = (A - B)(A + B). Here A is (798 + 579) and B is (798 - 579). After applying the identity, you should see heavy cancellation when dividing by 798 × 579.

Step-by-Step Solution:

Verification / Alternative check:

If you prefer a numerical cross check, you can compute the inner sums and differences first, then square them, but this is more time consuming. The algebraic identity is reliable and gives the same result.

Why Other Options Are Wrong:

The values 2, 6, 8, and 10 come from partial cancellation or incorrect application of the difference of squares formula. For example, using A^2 - B^2 = (A + B)^2 or forgetting to multiply both (A - B) and (A + B) leads to these incorrect values.

Common Pitfalls:

Some learners attempt full expansion of large squares, which is unnecessary and error prone. Others confuse the identity for (A + B)^2 with the identity for A^2 - B^2. Recognizing patterns quickly is essential for speed in competitive tests.

Final Answer:

The value of the expression is 4.