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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 260 · 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 56².
  2. 2.Use a² − b² = (a + b)(a − b) to find 54² − 8².
  3. 3.Use (a + b)(a − b) = a² − b² to find 44 × 36.
  4. 4.Use (a − b)² = a² − 2ab + b² to find 29².
  5. 5.Find the value of x² − y² when x = 13 and y = 8.
  6. 6.Use (a + b)(a − b) = a² − b² to find 23 × 17.
  7. 7.Use (a − b)² = a² − 2ab + b² to find 39².
  8. 8.Find the value of x² − 2xy + y² when x = 10 and y = 2.
  9. 9.Use (a + b)² = a² + 2ab + b² to find 12².
  10. 10.If a − b = 1 and ab = 56, what is a² + b²?
  11. 11.Use (a + b)² = a² + 2ab + b² to find 101².
  12. 12.Find the value of x² − y² when x = 7 and y = 1.
  13. 13.If a − b = 7 and ab = 44, what is a² + b²?
  14. 14.Use (a − b)² = a² − 2ab + b² to find 59².
  15. 15.If a − b = 1 and ab = 12, what is a² + b²?
  16. 16.If a + b = 5 and ab = 4, what is a² + b²?
  17. 17.Find the value of x² + 2xy + y² when x = 7 and y = 4.
  18. 18.Use a² − b² = (a + b)(a − b) to find 45² − 35².
  19. 19.Use (a + b)² = a² + 2ab + b² to find 41².
  20. 20.Find the value of x² − y² when x = 6 and y = 2.
  21. 21.Use a² − b² = (a + b)(a − b) to find 74² − 40².
  22. 22.Use (a − b)² = a² − 2ab + b² to find 23².
  23. 23.If a + b = 17 and ab = 70, what is a² + b²?
  24. 24.Use (a − b)² = a² − 2ab + b² to find 95².
  25. 25.Use a² − b² = (a + b)(a − b) to find 74² − 46².
  26. 26.Use (a + b)² = a² + 2ab + b² to find 67².
  27. 27.Find the value of x² − 2xy + y² when x = 12 and y = 2.
  28. 28.If a + b = 15 and ab = 54, what is a² + b²?
  29. 29.If a + b = 7 and ab = 6, what is a² + b²?
  30. 30.If a + b = 11 and ab = 30, what is a² + b²?
  31. 31.Use (a + b)² = a² + 2ab + b² to find 11².
  32. 32.Use (a − b)² = a² − 2ab + b² to find 17².
  33. 33.Use a² − b² = (a + b)(a − b) to find 96² − 94².
  34. 34.Use (a − b)² = a² − 2ab + b² to find 75².
  35. 35.If a + b = 21 and ab = 110, what is a² + b²?
  36. 36.Use (a + b)² = a² + 2ab + b² to find 45².
  37. 37.Use (a + b)(a − b) = a² − b² to find 67 × 53.
  38. 38.If a − b = 2 and ab = 80, what is a² + b²?
  39. 39.Use a² − b² = (a + b)(a − b) to find 69² − 35².
  40. 40.If a − b = 7 and ab = 8, what is a² + b²?

Answer key

  1. 3136
  2. 2852
  3. 1584
  4. 841
  5. 105
  6. 391
  7. 1521
  8. 64
  9. 144
  10. 113
  11. 10201
  12. 48
  13. 137
  14. 3481
  15. 25
  16. 17
  17. 121
  18. 800
  19. 1681
  20. 32
  21. 3876
  22. 529
  23. 149
  24. 9025
  25. 3360
  26. 4489
  27. 100
  28. 117
  29. 37
  30. 61
  31. 121
  32. 289
  33. 380
  34. 5625
  35. 221
  36. 2025
  37. 3551
  38. 164
  39. 3536
  40. 65

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