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Squaring 1

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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 1

  1. 1. Squaring – 1 (from Bhaskara’s Lilavati) Vinay Nair SCHOOL OF VEDIC MATHS
  2. 2. • (a + b)2 = a2 + 2ab + b2
  3. 3. a a a b a a a a a b b b a a b b b
  4. 4. a a b a a a a b b b a a b b b
  5. 5. a a b a a a a b b b a a b b b
  6. 6. a a b a a a a b b b a a b b b
  7. 7. (a + b)2 = a2 + 2ab + b2 a b a a b b a b
  8. 8. Geometric Representation (i) 132
  9. 9. Splitting a number (i) 132 (10 + 3)2
  10. 10. (i) 132 (10 + 3)2 The coloured part is 102
  11. 11. (i) 132 (10 + 3)2 The coloured part is 32
  12. 12. (i) 132 (10 + 3)2 Remaining parts are 10 x 3 = 30 and 10 x 3 = 30
  13. 13. (i) 132 (10 + 3)2
  14. 14. 102 + 10 x 3 + 10 x 3 + 32 = 100 = 30 = 30 = 9 169 2 a + 2ab + 2 b
  15. 15. More examples (ii) 242 (20 + 4)2 202 = 400 2 x 20 x 4 = 160 42 = 16 576
  16. 16. More examples (iii) 622 (60 + 2)2 602 = 3600 2 x 60 x 2 = 240 22 = 4 3844
  17. 17. More examples (iv) 382 (30 + 8)2 302 = 900 2 x 30 x 8 = 480 82 = 64 1444
  18. 18. More examples (v) 1252 (100 + 25)2 1002 2 x 100 x 25 252 = 10000 = 5000 = 625 15625
  19. 19. More examples (v) 1252 (120 + 5)2 1202 2 x 120 x 5 52 = 14400 = 1200 = 25 15625
  20. 20. Thank you!

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