Multiply 58 × 62 in one subtraction

Question

58 and 62 are mirror images around 60, each 2 away. Solve in your head. What is 58 	imes 62? Aim: under 8 seconds.

Accepted Answer

Midpoint 60, gap 2, so (60-2)(60+2) = 60^2 - 2^2: 58 	imes 62 = 3600 - 4 = 3596. So 58 	imes 62 = \mathbf{3596}. Nothing more than "thirty-six hundred minus four." Check by distributing: 58 	imes 62 = 58 	imes 60 + 58 	imes 2 = 3480 + 116 = 3596. Confirmed. Takeaway. Numbers straddling a round number by the same small gap collapse to 	ext{mid}^2 - 	ext{gap}^2. The smaller the gap, the more trivial the subtraction.

Multiply 58 × 62 in one subtraction

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