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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 599 · 40 sums
TalentJR

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.Find the value of x² − y² when x = 8 and y = 2.
  2. 2.Use (a − b)² = a² − 2ab + b² to find 21².
  3. 3.If a + b = 12 and ab = 32, what is a² + b²?
  4. 4.Use (a + b)(a − b) = a² − b² to find 97 × 83.
  5. 5.Use (a + b)² = a² + 2ab + b² to find 13².
  6. 6.Find the value of x² + 2xy + y² when x = 14 and y = 8.
  7. 7.Use (a + b)² = a² + 2ab + b² to find 16².
  8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 6.
  9. 9.Use (a + b)(a − b) = a² − b² to find 73 × 67.
  10. 10.Use (a + b)(a − b) = a² − b² to find 43 × 37.
  11. 11.Use (a + b)² = a² + 2ab + b² to find 21².
  12. 12.If a + b = 22 and ab = 120, what is a² + b²?
  13. 13.Use (a − b)² = a² − 2ab + b² to find 77².
  14. 14.If a + b = 11 and ab = 18, what is a² + b²?
  15. 15.Find the value of x² − y² when x = 14 and y = 12.
  16. 16.Use (a − b)² = a² − 2ab + b² to find 44².
  17. 17.Find the value of x² − y² when x = 10 and y = 9.
  18. 18.If a + b = 3 and ab = 2, what is a² + b²?
  19. 19.Use (a + b)² = a² + 2ab + b² to find 51².
  20. 20.Use (a − b)² = a² − 2ab + b² to find 19².
  21. 21.Use (a + b)(a − b) = a² − b² to find 25 × 15.
  22. 22.Use a² − b² = (a + b)(a − b) to find 84² − 45².
  23. 23.Use (a − b)² = a² − 2ab + b² to find 24².
  24. 24.Use (a − b)² = a² − 2ab + b² to find 64².
  25. 25.Find the value of x² + 2xy + y² when x = 14 and y = 2.
  26. 26.If a − b = 2 and ab = 35, what is a² + b²?
  27. 27.Use (a + b)(a − b) = a² − b² to find 22 × 18.
  28. 28.Use (a − b)² = a² − 2ab + b² to find 17².
  29. 29.If a + b = 7 and ab = 10, what is a² + b²?
  30. 30.Use (a − b)² = a² − 2ab + b² to find 63².
  31. 31.Use (a + b)² = a² + 2ab + b² to find 42².
  32. 32.Use (a + b)(a − b) = a² − b² to find 59 × 41.
  33. 33.Use a² − b² = (a + b)(a − b) to find 33² − 5².
  34. 34.Use (a + b)² = a² + 2ab + b² to find 85².
  35. 35.Use (a + b)² = a² + 2ab + b² to find 98².
  36. 36.Use (a + b)² = a² + 2ab + b² to find 23².
  37. 37.If a + b = 10 and ab = 9, what is a² + b²?
  38. 38.Use (a − b)² = a² − 2ab + b² to find 38².
  39. 39.Use (a − b)² = a² − 2ab + b² to find 83².
  40. 40.If a − b = 3 and ab = 4, what is a² + b²?

Answer key

  1. 60
  2. 441
  3. 80
  4. 8051
  5. 169
  6. 484
  7. 256
  8. 196
  9. 4891
  10. 1591
  11. 441
  12. 244
  13. 5929
  14. 85
  15. 52
  16. 1936
  17. 19
  18. 5
  19. 2601
  20. 361
  21. 375
  22. 5031
  23. 576
  24. 4096
  25. 256
  26. 74
  27. 396
  28. 289
  29. 29
  30. 3969
  31. 1764
  32. 2419
  33. 1064
  34. 7225
  35. 9604
  36. 529
  37. 82
  38. 1444
  39. 6889
  40. 17

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