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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 996 · 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.Find the value of x² − y² when x = 15 and y = 1.
  2. 2.Use (a + b)(a − b) = a² − b² to find 68 × 52.
  3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 1.
  4. 4.Use (a − b)² = a² − 2ab + b² to find 81².
  5. 5.If a − b = 1 and ab = 110, what is a² + b²?
  6. 6.Use a² − b² = (a + b)(a − b) to find 31² − 22².
  7. 7.Use (a − b)² = a² − 2ab + b² to find 79².
  8. 8.Use a² − b² = (a + b)(a − b) to find 39² − 27².
  9. 9.Use (a − b)² = a² − 2ab + b² to find 14².
  10. 10.Use (a − b)² = a² − 2ab + b² to find 71².
  11. 11.Use (a − b)² = a² − 2ab + b² to find 51².
  12. 12.Use (a + b)(a − b) = a² − b² to find 42 × 38.
  13. 13.If a − b = 3 and ab = 18, what is a² + b²?
  14. 14.Use (a + b)² = a² + 2ab + b² to find 63².
  15. 15.Find the value of x² − 2xy + y² when x = 6 and y = 5.
  16. 16.Find the value of x² − y² when x = 11 and y = 3.
  17. 17.Use a² − b² = (a + b)(a − b) to find 22² − 14².
  18. 18.Use (a − b)² = a² − 2ab + b² to find 41².
  19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 21².
  20. 20.If a + b = 10 and ab = 21, what is a² + b²?
  21. 21.Use (a + b)² = a² + 2ab + b² to find 59².
  22. 22.Use (a + b)² = a² + 2ab + b² to find 95².
  23. 23.Use (a + b)² = a² + 2ab + b² to find 69².
  24. 24.Find the value of x² − 2xy + y² when x = 8 and y = 2.
  25. 25.If a − b = 1 and ab = 12, what is a² + b²?
  26. 26.Find the value of x² + 2xy + y² when x = 13 and y = 7.
  27. 27.Use (a + b)(a − b) = a² − b² to find 84 × 76.
  28. 28.Find the value of x² + 2xy + y² when x = 8 and y = 2.
  29. 29.Use (a − b)² = a² − 2ab + b² to find 57².
  30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 1.
  31. 31.Find the value of x² + 2xy + y² when x = 6 and y = 5.
  32. 32.Use (a − b)² = a² − 2ab + b² to find 12².
  33. 33.Find the value of x² − y² when x = 14 and y = 2.
  34. 34.Use (a + b)(a − b) = a² − b² to find 92 × 88.
  35. 35.If a + b = 7 and ab = 6, what is a² + b²?
  36. 36.Find the value of x² + 2xy + y² when x = 7 and y = 2.
  37. 37.Use (a − b)² = a² − 2ab + b² to find 35².
  38. 38.If a − b = 1 and ab = 2, what is a² + b²?
  39. 39.If a − b = 2 and ab = 8, what is a² + b²?
  40. 40.If a − b = 2 and ab = 120, what is a² + b²?

Answer key

  1. 224
  2. 3536
  3. 9
  4. 6561
  5. 221
  6. 477
  7. 6241
  8. 792
  9. 196
  10. 5041
  11. 2601
  12. 1596
  13. 45
  14. 3969
  15. 1
  16. 112
  17. 288
  18. 1681
  19. 43
  20. 58
  21. 3481
  22. 9025
  23. 4761
  24. 36
  25. 25
  26. 400
  27. 6384
  28. 100
  29. 3249
  30. 4
  31. 121
  32. 144
  33. 192
  34. 8096
  35. 37
  36. 81
  37. 1225
  38. 5
  39. 20
  40. 244

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