Compute 35 × 45 in your head

Question

Solve in your head, no long multiplication. What is 35 	imes 45? Aim: under 5 seconds.

Accepted Answer

The midpoint of 35 and 45 is 40, and each is 5 away: they are 40 - 5 and 40 + 5. 35 	imes 45 = (40 - 5)(40 + 5) = 40^2 - 5^2 = 1600 - 25 = 1575. A larger gap (d = 5) just means a larger square to subtract; the method does not change. Check against the school method: 35 	imes 45 = 35 	imes 40 + 35 	imes 5 = 1400 + 175 = 1575. Same answer, more steps. Takeaway. The gap d can be 2, 3, or 5; all that matters is that the factors are equidistant from a midpoint you can square. Product = m^2 - d^2, one subtraction once you see it.

Compute 35 × 45 in your head

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