Same identity, but round to the nearest hundred instead of ten — a is now a two-digit number. Since a² isn't trivial anymore, apply the same trick to a itself, this time rounding it to the nearest ten.
512² = (512+12)(512−12) + 12²= 524 × 500 + 12²12² = (12+2)(12−2) + 2² = 14×10 + 4 = 144= 262 000 + 144 = 262 144
684² = (684+16)(684−16) + 16²= 700 × 668 + 16²16² = (16+4)(16−4) + 4² = 20×12 + 16 = 256= 467 600 + 256 = 467 856
a rounds to the nearest hundred either way — up here, down in the first example.
The live example below shows a simpler one-step version — round to the nearest ten instead of a hundred — which works for any digit count but produces less round factors than the full technique above.
?
Practice 3d²