The fast method
⚡
Centre 50, gap 2: 2500 - 4 = 2496.
How it works
Multiply (a-b)(a+b) by calculating a² - b². The cross terms cancel: a² + ab - ab - b² = a² - b².
Why it works
The cross terms cancel: a² + ab - ab - b² = a² - b².
Use it when
Both numbers must be equally far from the chosen centre.
Watch out for
Subtract the square of the gap, not the gap itself.
Verified examples
Example 1
48 × 52
Centre 50, gap 2: 2500 - 4 = 2496.
2496Example 2
29 × 31
Centre 30, gap 1: 900 - 1 = 899.
899Example 3
93 × 107
Centre 100, gap 7: 10000 - 49 = 9951.
9951