Multiply 43 × 37 with difference of squares

Question

The two factors are each 3 away from 40. That symmetry is a gift. Solve in your head. What is 43 	imes 37? Aim: under 10 seconds.

Accepted Answer

Their midpoint is (43+37)/2 = 40, and each sits 3 away, so apply (m+d)(m-d) = m^2 - d^2: 43 	imes 37 = 40^2 - 3^2 = 1600 - 9 = 1591. So 43 	imes 37 = \mathbf{1591}. Just "sixteen hundred minus nine." Spotting the midpoint is the whole game; once you see 40 in the middle, the rest is a reflex. Takeaway. Any two numbers with a round midpoint multiply as 	ext{mid}^2 - 	ext{gap}^2. Scan every product for a hidden difference of squares.

Multiply 43 × 37 with difference of squares

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