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Ūrdhva-Tiryagbhyāṃ — Vertically and crosswise

Ūrdhva-Tiryagbhyāṃ

ऊर्ध्व-तिर्यग्भ्याम्Urdhva-Tiryagbyham

Vertically and crosswise. Multiply digits vertically, then crosswise, then vertically again — the pattern forms an expanding diamond.

Why it works: For AB × CD: result = [A×C] [A×D + B×C] [B×D]. This is exactly the expansion of (10A+B)(10C+D) = 100AC + 10(AD+BC) + BD. The crosswise products fill the middle. For 3-digit: the diamond has 5 nodes matching 5 partial-product positions.

Speed advantage: Works for any digit count. Single mental pass with carries, no partial products written.

Best for

  • General multiplication — any two numbers
  • The universal Vedic multiplier

See the animated lesson, practice drills & proof on SutraFlow →

Originally published at https://www.sutraflow.app/sutras/urdhva-tiryagbyham

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