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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 606 · 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 12².
  2. 2.If a − b = 6 and ab = 7, what is a² + b²?
  3. 3.If a − b = 1 and ab = 2, what is a² + b²?
  4. 4.If a − b = 11 and ab = 12, what is a² + b²?
  5. 5.Use (a + b)² = a² + 2ab + b² to find 16².
  6. 6.If a + b = 4 and ab = 3, what is a² + b²?
  7. 7.Use (a + b)(a − b) = a² − b² to find 103 × 97.
  8. 8.Use (a − b)² = a² − 2ab + b² to find 86².
  9. 9.Find the value of x² + 2xy + y² when x = 7 and y = 4.
  10. 10.If a + b = 12 and ab = 27, what is a² + b²?
  11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
  12. 12.Use a² − b² = (a + b)(a − b) to find 44² − 38².
  13. 13.Find the value of x² − 2xy + y² when x = 8 and y = 2.
  14. 14.Find the value of x² − y² when x = 9 and y = 8.
  15. 15.Use (a − b)² = a² − 2ab + b² to find 35².
  16. 16.If a + b = 17 and ab = 66, what is a² + b²?
  17. 17.If a − b = 1 and ab = 6, what is a² + b²?
  18. 18.Use (a + b)² = a² + 2ab + b² to find 64².
  19. 19.Use a² − b² = (a + b)(a − b) to find 41² − 25².
  20. 20.Use (a + b)² = a² + 2ab + b² to find 22².
  21. 21.Find the value of x² − 2xy + y² when x = 9 and y = 6.
  22. 22.If a + b = 14 and ab = 48, what is a² + b²?
  23. 23.If a + b = 3 and ab = 2, what is a² + b²?
  24. 24.Use a² − b² = (a + b)(a − b) to find 33² − 1².
  25. 25.Use (a − b)² = a² − 2ab + b² to find 58².
  26. 26.Use a² − b² = (a + b)(a − b) to find 96² − 76².
  27. 27.Use (a − b)² = a² − 2ab + b² to find 68².
  28. 28.If a + b = 19 and ab = 88, what is a² + b²?
  29. 29.Use a² − b² = (a + b)(a − b) to find 27² − 25².
  30. 30.Use (a + b)² = a² + 2ab + b² to find 36².
  31. 31.Use (a + b)² = a² + 2ab + b² to find 46².
  32. 32.Find the value of x² + 2xy + y² when x = 15 and y = 6.
  33. 33.Use (a − b)² = a² − 2ab + b² to find 21².
  34. 34.Find the value of x² − y² when x = 15 and y = 11.
  35. 35.Use (a + b)² = a² + 2ab + b² to find 67².
  36. 36.Use (a − b)² = a² − 2ab + b² to find 84².
  37. 37.Use (a + b)(a − b) = a² − b² to find 87 × 73.
  38. 38.Use a² − b² = (a + b)(a − b) to find 34² − 22².
  39. 39.Use (a + b)² = a² + 2ab + b² to find 106².
  40. 40.Use (a + b)(a − b) = a² − b² to find 47 × 33.

Answer key

  1. 144
  2. 50
  3. 5
  4. 145
  5. 256
  6. 10
  7. 9991
  8. 7396
  9. 121
  10. 90
  11. 361
  12. 492
  13. 36
  14. 17
  15. 1225
  16. 157
  17. 13
  18. 4096
  19. 1056
  20. 484
  21. 9
  22. 100
  23. 5
  24. 1088
  25. 3364
  26. 3440
  27. 4624
  28. 185
  29. 104
  30. 1296
  31. 2116
  32. 441
  33. 441
  34. 104
  35. 4489
  36. 7056
  37. 6351
  38. 672
  39. 11236
  40. 1551

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