Multiply 106 by 94 in your head

Question

Solve in your head. What is 106 	imes 94? Aim: under 10 seconds.

Accepted Answer

The two numbers are symmetric around 100: 100 + 6 and 100 - 6. That is exactly the difference-of-squares pattern (a+b)(a-b) = a^2 - b^2 with a = 100, b = 6: 106 	imes 94 = 100^2 - 6^2 = 10{,}000 - 36 = 9{,}964. Spotting that a product straddles a round number by an equal amount is the whole trick. It turns an awkward two-digit-by-three-digit multiplication into one subtraction. The same idea squares near-round numbers: 103 	imes 97 = 10{,}000 - 9 = 9{,}991, and 58 	imes 62 = 60^2 - 2^2 = 3{,}600 - 4 = 3{,}596. Takeaway. When two factors sit an equal distance either side of a round number a…

Multiply 106 by 94 in your head

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