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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 346 · 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)(a − b) = a² − b² to find 77 × 63.
  2. 2.Use (a + b)² = a² + 2ab + b² to find 18².
  3. 3.Find the value of x² + 2xy + y² when x = 14 and y = 2.
  4. 4.If a − b = 1 and ab = 20, what is a² + b²?
  5. 5.If a + b = 5 and ab = 6, what is a² + b²?
  6. 6.If a − b = 5 and ab = 6, what is a² + b²?
  7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
  8. 8.Use (a + b)² = a² + 2ab + b² to find 73².
  9. 9.Use (a + b)² = a² + 2ab + b² to find 81².
  10. 10.Use (a + b)(a − b) = a² − b² to find 21 × 19.
  11. 11.Find the value of x² − y² when x = 15 and y = 13.
  12. 12.Use (a − b)² = a² − 2ab + b² to find 47².
  13. 13.Use (a + b)² = a² + 2ab + b² to find 55².
  14. 14.Use (a − b)² = a² − 2ab + b² to find 61².
  15. 15.If a − b = 1 and ab = 2, what is a² + b²?
  16. 16.Use a² − b² = (a + b)(a − b) to find 36² − 27².
  17. 17.Use (a + b)² = a² + 2ab + b² to find 37².
  18. 18.Find the value of x² − y² when x = 6 and y = 4.
  19. 19.Find the value of x² − y² when x = 8 and y = 7.
  20. 20.Use (a + b)² = a² + 2ab + b² to find 42².
  21. 21.Use (a − b)² = a² − 2ab + b² to find 68².
  22. 22.Use (a + b)(a − b) = a² − b² to find 108 × 92.
  23. 23.If a + b = 4 and ab = 3, what is a² + b²?
  24. 24.Use (a + b)² = a² + 2ab + b² to find 106².
  25. 25.Use (a − b)² = a² − 2ab + b² to find 92².
  26. 26.Find the value of x² − y² when x = 15 and y = 8.
  27. 27.Find the value of x² − y² when x = 7 and y = 2.
  28. 28.Find the value of x² − 2xy + y² when x = 5 and y = 4.
  29. 29.Use (a + b)² = a² + 2ab + b² to find 53².
  30. 30.Find the value of x² − y² when x = 12 and y = 5.
  31. 31.Use (a − b)² = a² − 2ab + b² to find 94².
  32. 32.If a − b = 4 and ab = 32, what is a² + b²?
  33. 33.Use a² − b² = (a + b)(a − b) to find 39² − 22².
  34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 1.
  35. 35.Use (a + b)(a − b) = a² − b² to find 53 × 47.
  36. 36.Use (a + b)² = a² + 2ab + b² to find 25².
  37. 37.Use (a + b)² = a² + 2ab + b² to find 34².
  38. 38.Use (a − b)² = a² − 2ab + b² to find 53².
  39. 39.Use (a + b)² = a² + 2ab + b² to find 96².
  40. 40.Use (a + b)² = a² + 2ab + b² to find 108².

Answer key

  1. 4851
  2. 324
  3. 256
  4. 41
  5. 13
  6. 37
  7. 3721
  8. 5329
  9. 6561
  10. 399
  11. 56
  12. 2209
  13. 3025
  14. 3721
  15. 5
  16. 567
  17. 1369
  18. 20
  19. 15
  20. 1764
  21. 4624
  22. 9936
  23. 10
  24. 11236
  25. 8464
  26. 161
  27. 45
  28. 1
  29. 2809
  30. 119
  31. 8836
  32. 80
  33. 1037
  34. 25
  35. 2491
  36. 625
  37. 1156
  38. 2809
  39. 9216
  40. 11664

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