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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 434 · 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 a² − b² = (a + b)(a − b) to find 51² − 34².
  2. 2.Use a² − b² = (a + b)(a − b) to find 88² − 49².
  3. 3.Find the value of x² + 2xy + y² when x = 4 and y = 3.
  4. 4.Use (a + b)² = a² + 2ab + b² to find 23².
  5. 5.Use (a + b)(a − b) = a² − b² to find 81 × 79.
  6. 6.Use (a + b)² = a² + 2ab + b² to find 54².
  7. 7.Use a² − b² = (a + b)(a − b) to find 46² − 19².
  8. 8.If a − b = 3 and ab = 108, what is a² + b²?
  9. 9.Find the value of x² − y² when x = 7 and y = 3.
  10. 10.If a + b = 19 and ab = 84, what is a² + b²?
  11. 11.If a − b = 3 and ab = 18, what is a² + b²?
  12. 12.Find the value of x² − y² when x = 3 and y = 2.
  13. 13.Use (a + b)² = a² + 2ab + b² to find 103².
  14. 14.Use (a − b)² = a² − 2ab + b² to find 42².
  15. 15.Use (a − b)² = a² − 2ab + b² to find 62².
  16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
  17. 17.Use (a + b)² = a² + 2ab + b² to find 88².
  18. 18.If a + b = 3 and ab = 2, what is a² + b²?
  19. 19.Find the value of x² − 2xy + y² when x = 7 and y = 4.
  20. 20.Find the value of x² − y² when x = 7 and y = 2.
  21. 21.Use (a − b)² = a² − 2ab + b² to find 58².
  22. 22.Use (a + b)² = a² + 2ab + b² to find 37².
  23. 23.Find the value of x² + 2xy + y² when x = 6 and y = 5.
  24. 24.Use (a + b)² = a² + 2ab + b² to find 101².
  25. 25.Find the value of x² − y² when x = 6 and y = 2.
  26. 26.Use (a + b)² = a² + 2ab + b² to find 61².
  27. 27.Use (a + b)² = a² + 2ab + b² to find 82².
  28. 28.Use (a + b)² = a² + 2ab + b² to find 83².
  29. 29.Use (a − b)² = a² − 2ab + b² to find 35².
  30. 30.If a + b = 20 and ab = 99, what is a² + b²?
  31. 31.Use (a − b)² = a² − 2ab + b² to find 96².
  32. 32.Use (a + b)² = a² + 2ab + b² to find 109².
  33. 33.Use a² − b² = (a + b)(a − b) to find 92² − 78².
  34. 34.Use (a + b)² = a² + 2ab + b² to find 45².
  35. 35.Find the value of x² − 2xy + y² when x = 7 and y = 2.
  36. 36.Use (a + b)² = a² + 2ab + b² to find 32².
  37. 37.Use (a − b)² = a² − 2ab + b² to find 97².
  38. 38.Use (a + b)² = a² + 2ab + b² to find 96².
  39. 39.Use a² − b² = (a + b)(a − b) to find 36² − 8².
  40. 40.Use a² − b² = (a + b)(a − b) to find 58² − 36².

Answer key

  1. 1445
  2. 5343
  3. 49
  4. 529
  5. 6399
  6. 2916
  7. 1755
  8. 225
  9. 40
  10. 193
  11. 45
  12. 5
  13. 10609
  14. 1764
  15. 3844
  16. 5184
  17. 7744
  18. 5
  19. 9
  20. 45
  21. 3364
  22. 1369
  23. 121
  24. 10201
  25. 32
  26. 3721
  27. 6724
  28. 6889
  29. 1225
  30. 202
  31. 9216
  32. 11881
  33. 2380
  34. 2025
  35. 25
  36. 1024
  37. 9409
  38. 9216
  39. 1232
  40. 2068

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