Evaluate: 107 × 107 + 93 × 93. What is the value?

Given data

• Compute 107² + 93².

Concept / Approach

• Square each term separately and add; or use identities to cross-check.
• Useful identity for verification: (a + b)² = a² + 2ab + b² ⇒ a² + b² = (a + b)² − 2ab.

Step-by-step calculation

107² = 11,44993² = 8,649Sum = 11,449 + 8,649 = 20,098

Verification / Alternative

(107 + 93)² − 2·107·93 = 200² − 2·9,951 = 40,000 − 19,902 = 20,098

Common pitfalls

• Arithmetic slip while squaring near round numbers; always verify with an identity.

Final Answer

20098