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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 22 · 40 sums
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The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

NameDateTime takenScore ___ / 40
  1. 1.Use (a − b)² = a² − 2ab + b² to find 99².
  2. 2.Use (a + b)² = a² + 2ab + b² to find 103².
  3. 3.Use (a − b)² = a² − 2ab + b² to find 67².
  4. 4.Use (a − b)² = a² − 2ab + b² to find 11².
  5. 5.Use (a − b)² = a² − 2ab + b² to find 22².
  6. 6.Use (a − b)² = a² − 2ab + b² to find 77².
  7. 7.Use (a − b)² = a² − 2ab + b² to find 49².
  8. 8.If a − b = 1 and ab = 12, what is a² + b²?
  9. 9.Use (a + b)² = a² + 2ab + b² to find 108².
  10. 10.If a − b = 1 and ab = 30, what is a² + b²?
  11. 11.Use a² − b² = (a + b)(a − b) to find 62² − 6².
  12. 12.Use a² − b² = (a + b)(a − b) to find 30² − 21².
  13. 13.Find the value of x² + 2xy + y² when x = 14 and y = 11.
  14. 14.Use (a + b)(a − b) = a² − b² to find 32 × 28.
  15. 15.Use (a + b)² = a² + 2ab + b² to find 82².
  16. 16.Use a² − b² = (a + b)(a − b) to find 68² − 64².
  17. 17.If a − b = 5 and ab = 14, what is a² + b²?
  18. 18.Find the value of x² + 2xy + y² when x = 9 and y = 1.
  19. 19.Use a² − b² = (a + b)(a − b) to find 64² − 61².
  20. 20.Use (a + b)² = a² + 2ab + b² to find 62².
  21. 21.Use (a + b)² = a² + 2ab + b² to find 102².
  22. 22.If a + b = 3 and ab = 2, what is a² + b²?
  23. 23.If a − b = 3 and ab = 18, what is a² + b²?
  24. 24.Use a² − b² = (a + b)(a − b) to find 26² − 6².
  25. 25.If a − b = 2 and ab = 3, what is a² + b²?
  26. 26.Find the value of x² − y² when x = 9 and y = 5.
  27. 27.Use (a + b)(a − b) = a² − b² to find 38 × 22.
  28. 28.If a − b = 5 and ab = 50, what is a² + b²?
  29. 29.Use (a + b)² = a² + 2ab + b² to find 27².
  30. 30.Use (a − b)² = a² − 2ab + b² to find 38².
  31. 31.If a − b = 3 and ab = 4, what is a² + b²?
  32. 32.Use a² − b² = (a + b)(a − b) to find 97² − 84².
  33. 33.Use (a − b)² = a² − 2ab + b² to find 32².
  34. 34.Use (a − b)² = a² − 2ab + b² to find 36².
  35. 35.If a − b = 1 and ab = 42, what is a² + b²?
  36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
  37. 37.Find the value of x² − y² when x = 9 and y = 7.
  38. 38.Use a² − b² = (a + b)(a − b) to find 24² − 19².
  39. 39.Use (a − b)² = a² − 2ab + b² to find 51².
  40. 40.Use (a + b)(a − b) = a² − b² to find 54 × 46.

Answer key

  1. 9801
  2. 10609
  3. 4489
  4. 121
  5. 484
  6. 5929
  7. 2401
  8. 25
  9. 11664
  10. 61
  11. 3808
  12. 459
  13. 625
  14. 896
  15. 6724
  16. 528
  17. 53
  18. 100
  19. 375
  20. 3844
  21. 10404
  22. 5
  23. 45
  24. 640
  25. 10
  26. 56
  27. 836
  28. 125
  29. 729
  30. 1444
  31. 17
  32. 2353
  33. 1024
  34. 1296
  35. 85
  36. 169
  37. 32
  38. 215
  39. 2601
  40. 2484

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