Compute 97 × 103 in your head

Question

Solve in your head. What is 97 	imes 103? Aim: under 10 seconds.

Accepted Answer

The factors straddle 100 at distance 3, so difference of squares makes this almost instant: 97 	imes 103 = 100^2 - 3^2 = 10000 - 9 = 9991. Compare the grind: 97 	imes 103 = 97 	imes 100 + 97 	imes 3 = 9700 + 291 = 9991. Same answer, but you had to compute and add 291. With the midpoint at a clean 100 and a small offset, the squares route is the obvious winner. Takeaway. Products of the form (m - d)(m + d) around a round midpoint m equal m^2 - d^2. Numbers near 100 (or 1000) with a small symmetric offset are the ideal case: the big square is trivial and the correction is a tiny square.

Compute 97 × 103 in your head

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