What is Arthur Benjamin's all-purpose squaring method, A² = (A+d)(A−d) + d²?

Nudge A by d to the nearest multiple of ten, multiply the rounded-up and rounded-down numbers, then add d².

Since A² = (A + d)(A − d) + d², choosing d to round A makes one factor a round number:

• 37² → d = 3: (40)(34) + 9 = 1360 + 9 = 1369.
• 48² → d = 2: (50)(46) + 4 = 2300 + 4 = 2304.

Check: 37² = 1369. ✓ This works for any number, so it's the general fallback — the "near 50" and "near 100" shortcuts are just this with A rounded to 50 or 100.