Compute 96 × 104 in your head

Question

Solve in your head, no long multiplication. What is 96 	imes 104? Aim: under 5 seconds.

Accepted Answer

Both numbers straddle 100: they are 100 - 4 and 100 + 4. 96 	imes 104 = (100 - 4)(100 + 4) = 100^2 - 4^2 = 10000 - 16 = 9984. Centering on 100 is the easiest case of all, the square is just "1 with four zeros," so you only subtract 16. The long way, 96 	imes 104 = 96 	imes 100 + 96 	imes 4 = 9600 + 384 = 9984, confirms it. Takeaway. Numbers hugging 100 (or 1000) are prime targets: m^2 is trivial and the correction d^2 is small. Product = m^2 - d^2 turns a three-digit multiplication into a single subtraction.

Compute 96 × 104 in your head

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