The sum of two numbers is 25 and their difference is 13. What is their product?

Problem restatement
Given S = x + y = 25 and D = x − y = 13, find xy.

Concept/Approach
Use the identity S² − D² = 4xy.

Step-by-Step calculation
xy = (S² − D²) ÷ 4 = (25² − 13²) ÷ 4= (625 − 169) ÷ 4 = 456 ÷ 4 = 114

Verification/Alternative
Explicit solution: x = (S + D)÷2 = 19, y = (S − D)÷2 = 6 ⇒ xy = 114.

Common pitfalls
Computing (S − D)² instead of S² − D², or dividing by 2 instead of 4.

Final Answer
114