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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 243 · 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 15².
  2. 2.Find the value of x² − y² when x = 8 and y = 5.
  3. 3.If a + b = 11 and ab = 30, what is a² + b²?
  4. 4.Use (a − b)² = a² − 2ab + b² to find 75².
  5. 5.Find the value of x² − y² when x = 12 and y = 4.
  6. 6.Use (a − b)² = a² − 2ab + b² to find 73².
  7. 7.Use (a + b)² = a² + 2ab + b² to find 27².
  8. 8.If a − b = 7 and ab = 18, what is a² + b²?
  9. 9.Use (a + b)(a − b) = a² − b² to find 54 × 46.
  10. 10.Use (a + b)(a − b) = a² − b² to find 101 × 99.
  11. 11.Use a² − b² = (a + b)(a − b) to find 25² − 18².
  12. 12.If a + b = 8 and ab = 7, what is a² + b²?
  13. 13.Use (a + b)² = a² + 2ab + b² to find 61².
  14. 14.Use (a + b)² = a² + 2ab + b² to find 37².
  15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 3.
  16. 16.Use (a + b)² = a² + 2ab + b² to find 25².
  17. 17.Use (a + b)(a − b) = a² − b² to find 29 × 11.
  18. 18.Use (a + b)(a − b) = a² − b² to find 32 × 28.
  19. 19.If a + b = 5 and ab = 6, what is a² + b²?
  20. 20.Find the value of x² + 2xy + y² when x = 13 and y = 4.
  21. 21.If a + b = 9 and ab = 20, what is a² + b²?
  22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 7.
  23. 23.Use (a + b)² = a² + 2ab + b² to find 69².
  24. 24.Use (a − b)² = a² − 2ab + b² to find 22².
  25. 25.Find the value of x² − y² when x = 8 and y = 4.
  26. 26.Use (a − b)² = a² − 2ab + b² to find 19².
  27. 27.Use (a − b)² = a² − 2ab + b² to find 95².
  28. 28.Use (a − b)² = a² − 2ab + b² to find 66².
  29. 29.Use (a + b)² = a² + 2ab + b² to find 63².
  30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 1.
  31. 31.Use (a + b)² = a² + 2ab + b² to find 13².
  32. 32.Use a² − b² = (a + b)(a − b) to find 34² − 17².
  33. 33.Use (a + b)² = a² + 2ab + b² to find 52².
  34. 34.If a − b = 1 and ab = 2, what is a² + b²?
  35. 35.Use (a + b)² = a² + 2ab + b² to find 58².
  36. 36.Use (a − b)² = a² − 2ab + b² to find 17².
  37. 37.Use (a − b)² = a² − 2ab + b² to find 86².
  38. 38.Use (a + b)(a − b) = a² − b² to find 68 × 52.
  39. 39.Use (a + b)² = a² + 2ab + b² to find 77².
  40. 40.Use (a + b)² = a² + 2ab + b² to find 66².

Answer key

  1. 225
  2. 39
  3. 61
  4. 5625
  5. 128
  6. 5329
  7. 729
  8. 85
  9. 2484
  10. 9999
  11. 301
  12. 50
  13. 3721
  14. 1369
  15. 196
  16. 625
  17. 319
  18. 896
  19. 13
  20. 289
  21. 41
  22. 289
  23. 4761
  24. 484
  25. 48
  26. 361
  27. 9025
  28. 4356
  29. 3969
  30. 4
  31. 169
  32. 867
  33. 2704
  34. 5
  35. 3364
  36. 289
  37. 7396
  38. 3536
  39. 5929
  40. 4356

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