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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 720 · 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 83².
  2. 2.If a − b = 6 and ab = 7, what is a² + b²?
  3. 3.Use (a + b)(a − b) = a² − b² to find 32 × 28.
  4. 4.Use (a + b)² = a² + 2ab + b² to find 72².
  5. 5.Find the value of x² − 2xy + y² when x = 11 and y = 9.
  6. 6.Use (a − b)² = a² − 2ab + b² to find 39².
  7. 7.Find the value of x² − 2xy + y² when x = 6 and y = 5.
  8. 8.Use (a − b)² = a² − 2ab + b² to find 67².
  9. 9.Use (a − b)² = a² − 2ab + b² to find 15².
  10. 10.Use (a − b)² = a² − 2ab + b² to find 17².
  11. 11.Use (a − b)² = a² − 2ab + b² to find 72².
  12. 12.If a − b = 2 and ab = 3, what is a² + b²?
  13. 13.If a + b = 14 and ab = 45, what is a² + b²?
  14. 14.If a − b = 3 and ab = 40, what is a² + b²?
  15. 15.Use (a + b)(a − b) = a² − b² to find 104 × 96.
  16. 16.Use (a + b)² = a² + 2ab + b² to find 42².
  17. 17.Use (a + b)² = a² + 2ab + b² to find 58².
  18. 18.Use (a + b)(a − b) = a² − b² to find 47 × 33.
  19. 19.Use a² − b² = (a + b)(a − b) to find 31² − 8².
  20. 20.Find the value of x² − 2xy + y² when x = 9 and y = 6.
  21. 21.Find the value of x² + 2xy + y² when x = 10 and y = 2.
  22. 22.Use (a + b)(a − b) = a² − b² to find 22 × 18.
  23. 23.Use (a + b)(a − b) = a² − b² to find 44 × 36.
  24. 24.Use (a − b)² = a² − 2ab + b² to find 13².
  25. 25.Use a² − b² = (a + b)(a − b) to find 99² − 20².
  26. 26.Use (a + b)² = a² + 2ab + b² to find 37².
  27. 27.Use (a − b)² = a² − 2ab + b² to find 94².
  28. 28.If a + b = 5 and ab = 6, what is a² + b²?
  29. 29.Find the value of x² − 2xy + y² when x = 12 and y = 4.
  30. 30.Use a² − b² = (a + b)(a − b) to find 67² − 57².
  31. 31.Use (a − b)² = a² − 2ab + b² to find 32².
  32. 32.Use a² − b² = (a + b)(a − b) to find 54² − 34².
  33. 33.Find the value of x² − 2xy + y² when x = 12 and y = 2.
  34. 34.If a + b = 14 and ab = 24, what is a² + b²?
  35. 35.Use (a + b)² = a² + 2ab + b² to find 85².
  36. 36.Use (a + b)(a − b) = a² − b² to find 46 × 34.
  37. 37.Use (a + b)² = a² + 2ab + b² to find 95².
  38. 38.Find the value of x² − 2xy + y² when x = 6 and y = 2.
  39. 39.If a + b = 6 and ab = 8, what is a² + b²?
  40. 40.Use (a − b)² = a² − 2ab + b² to find 36².

Answer key

  1. 6889
  2. 50
  3. 896
  4. 5184
  5. 4
  6. 1521
  7. 1
  8. 4489
  9. 225
  10. 289
  11. 5184
  12. 10
  13. 106
  14. 89
  15. 9984
  16. 1764
  17. 3364
  18. 1551
  19. 897
  20. 9
  21. 144
  22. 396
  23. 1584
  24. 169
  25. 9401
  26. 1369
  27. 8836
  28. 13
  29. 64
  30. 1240
  31. 1024
  32. 1760
  33. 100
  34. 148
  35. 7225
  36. 1564
  37. 9025
  38. 16
  39. 20
  40. 1296

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