Multiply 91 × 89 the fast way

Question

91 and 89 bracket 90 by exactly 1 each. Solve in your head. What is 91 	imes 89? Aim: under 8 seconds.

Accepted Answer

Midpoint 90, gap 1, so (90+1)(90-1) = 90^2 - 1: 91 	imes 89 = 8100 - 1 = 8099. So 91 	imes 89 = \mathbf{8099}. Since you already know 90^2 = 8100, subtract 1 and you're done. This is the simplest case of difference of squares: two numbers one apart around a round center. Takeaway. (b+1)(b-1) = b^2 - 1. Products of a round number's two immediate neighbours are always "square minus one."

Multiply 91 × 89 the fast way

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