Explanation

Since a > b > c are the sides of a right triangle with a the largest side, a is the hypotenuse and a² = b² + c². Grouping the factors, (a + b + c)(a − b − c) = a² − (b + c)² and (a + b − c)(a − b + c) = (a + (b − c))(a − (b − c)) = a² − (b − c)²; multiplying and substituting a² = b² + c², the product simplifies to −4b²c². (Equivalently, the first three factors times −(a − b − c) form 16Δ² = 4b²c² by Heron's formula, and the extra minus sign gives −4b²c².) Hence option (b). Distractor (a) 4b²c² misses the sign from the factor (a − b − c) = −(−a + b + c), while (c) and (d) use the wrong pair of legs.