Compute 57 × 63 in your head

Question

Solve in your head, no long multiplication. What is 57 	imes 63? Aim: under 5 seconds.

Accepted Answer

The two numbers straddle 60: they are 60 - 3 and 60 + 3. 57 	imes 63 = (60 - 3)(60 + 3) = 60^2 - 3^2 = 3600 - 9 = 3591. The only thing you memorize is the square of the midpoint (60^2 = 3600); the rest is subtracting 9. This works around any convenient center, not just 50: find the number halfway between the two factors and check they are equidistant. Takeaway. The midpoint does not have to be a round multiple of 50. Whenever the two factors are symmetric about some m you can square quickly, the product is m^2 - d^2.

Compute 57 × 63 in your head

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