Compute 48 × 52 in your head

Question

Solve in your head, no paper, no long multiplication. What is 48 	imes 52? Aim: under 5 seconds.

Accepted Answer

Both numbers sit symmetrically around 50: they are 50 - 2 and 50 + 2. 48 	imes 52 = (50-2)(50+2) = 50^2 - 2^2 = 2500 - 4 = 2496 The slow route, 48 	imes 50 + 48 	imes 2 = 2400 + 96, also works, but the difference-of-squares route is a single subtraction once you see the midpoint. Takeaway. Whenever two factors have an easy midpoint m and are d apart from it, the product is m^2 - d^2. Scan every 2-digit multiplication for this pattern first, it turns products into one subtraction.

Compute 48 × 52 in your head

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