Video narration
Can you find 42 times 58 without using long multiplication? Picture a number line with 50 right in the middle. Forty-two sits eight steps to the left, and fifty-eight sits eight steps to the right. They're balanced: one is eight below 50, the other is eight above it. Now use that balance. Instead of multiplying the two numbers the long way, pair the offsets: take fifty minus eight, times fifty plus eight. On the number line, one side's extra eight is exactly matched by the other side's missing eight. So the product of fifty minus eight and fifty plus eight is fifty squared minus eight squared. That leaves fifty times fifty, or 2,500, minus eight times eight, or 64. Subtract: 2,500 minus 64 equals 2,436. Yes-the equal eight-step offsets around 50 make 42 times 58 equal 2,436.