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Squaring 2

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Have you ever wondered why is (a-b)^2 = a^2 - 2ab + b^2? Here is a presentation that will explain this algebraic identity. This was one of the algebraic identities that ancient Indian mathematician Bhaskaracharya-II (1114-1193 CE) gave in his mathematical treatise 'Lilavati' (1150 CE)

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Squaring 2

  1. 1. Squaring – 2 (from Bhaskara’s Lilavati) Vinay Nair SCHOOL OF VEDIC MATHS
  2. 2. • (a - b)2 = a2 - 2ab + b2
  3. 3. Geometric Representation (i) 82
  4. 4. (i) 82 (10 - 2)2
  5. 5. (i) 82 (10 - 2)2
  6. 6. (i) 82 (10 - 2)2
  7. 7. 102 - 10 x 2 - 10 x 2 + 22 = 100 = 20 = 20 = 4 64 100 – 2 x 20 + 4 = 64
  8. 8. More examples (ii) 292 (30 - 1)2 302 = 900 - 2 x 30 x 1 = -60 840 + 12 = 1 841
  9. 9. More examples (iii) 472 (50 - 3)2 502 = 2500 - 2 x 50 x 3 = -300 2200 + 32 = 9 2209
  10. 10. More examples (iv) 1922 (200 - 8)2 2002 - 2 x 200 x 8 + 82 = 40000 = -3200 36800 = 64 36864
  11. 11. More examples (v) 2472 (250 - 3)2 2502 - 2 x 250 x 3 + 32 = 62500 = -1500 61000 = 9 61009
  12. 12. Thank you!

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