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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 559 · 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 96².
  2. 2.Use (a − b)² = a² − 2ab + b² to find 87².
  3. 3.Use (a − b)² = a² − 2ab + b² to find 64².
  4. 4.Use (a + b)(a − b) = a² − b² to find 94 × 86.
  5. 5.Use (a − b)² = a² − 2ab + b² to find 48².
  6. 6.Use (a − b)² = a² − 2ab + b² to find 39².
  7. 7.Find the value of x² − y² when x = 14 and y = 8.
  8. 8.Use (a + b)² = a² + 2ab + b² to find 74².
  9. 9.Use (a + b)² = a² + 2ab + b² to find 24².
  10. 10.Use (a − b)² = a² − 2ab + b² to find 61².
  11. 11.If a + b = 13 and ab = 30, what is a² + b²?
  12. 12.Use (a + b)² = a² + 2ab + b² to find 31².
  13. 13.Use (a + b)² = a² + 2ab + b² to find 58².
  14. 14.Use (a + b)(a − b) = a² − b² to find 79 × 61.
  15. 15.Find the value of x² − 2xy + y² when x = 15 and y = 5.
  16. 16.Use (a + b)(a − b) = a² − b² to find 74 × 66.
  17. 17.Use (a − b)² = a² − 2ab + b² to find 58².
  18. 18.If a − b = 4 and ab = 21, what is a² + b²?
  19. 19.Use (a − b)² = a² − 2ab + b² to find 28².
  20. 20.If a − b = 8 and ab = 9, what is a² + b²?
  21. 21.Use (a − b)² = a² − 2ab + b² to find 25².
  22. 22.Use (a + b)(a − b) = a² − b² to find 57 × 43.
  23. 23.Use (a + b)(a − b) = a² − b² to find 76 × 64.
  24. 24.Use (a + b)² = a² + 2ab + b² to find 87².
  25. 25.Use (a + b)(a − b) = a² − b² to find 72 × 68.
  26. 26.Use (a + b)(a − b) = a² − b² to find 102 × 98.
  27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 2.
  28. 28.Find the value of x² − y² when x = 6 and y = 2.
  29. 29.If a − b = 3 and ab = 40, what is a² + b²?
  30. 30.Use (a − b)² = a² − 2ab + b² to find 23².
  31. 31.Find the value of x² − y² when x = 7 and y = 5.
  32. 32.Find the value of x² − y² when x = 7 and y = 3.
  33. 33.Use (a + b)² = a² + 2ab + b² to find 109².
  34. 34.Use (a − b)² = a² − 2ab + b² to find 75².
  35. 35.Find the value of x² − 2xy + y² when x = 8 and y = 7.
  36. 36.If a − b = 1 and ab = 2, what is a² + b²?
  37. 37.Use (a + b)² = a² + 2ab + b² to find 18².
  38. 38.Find the value of x² + 2xy + y² when x = 7 and y = 1.
  39. 39.Use (a + b)² = a² + 2ab + b² to find 37².
  40. 40.Use (a − b)² = a² − 2ab + b² to find 15².

Answer key

  1. 9216
  2. 7569
  3. 4096
  4. 8084
  5. 2304
  6. 1521
  7. 132
  8. 5476
  9. 576
  10. 3721
  11. 109
  12. 961
  13. 3364
  14. 4819
  15. 100
  16. 4884
  17. 3364
  18. 58
  19. 784
  20. 82
  21. 625
  22. 2451
  23. 4864
  24. 7569
  25. 4896
  26. 9996
  27. 49
  28. 32
  29. 89
  30. 529
  31. 24
  32. 40
  33. 11881
  34. 5625
  35. 1
  36. 5
  37. 324
  38. 64
  39. 1369
  40. 225

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