Compute 48 × 52 in your head

Question

Solve in your head. What is 48 	imes 52? Aim: under 10 seconds.

Accepted Answer

Route 1, difference of squares. The factors straddle 50 at distance 2, so 48 	imes 52 = 50^2 - 2^2 = 2500 - 4 = 2496. Route 2, round and correct. 48 	imes 52 = 48 	imes 50 + 48 	imes 2 = 2400 + 96 = 2496. Here Route 1 wins easily: the offset 2 is tiny, so 2^2 = 4 is trivial to subtract, whereas Route 2 makes you carry a 96. Takeaway. Whenever two factors are equally spaced around a round midpoint, reach for a 	imes b = m^2 - d^2 with m the midpoint and d the half-gap. The smaller the gap, the more this beats grinding out a partial-products multiplication.

Compute 48 × 52 in your head

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