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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 241 · 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 34².
  2. 2.Use (a + b)² = a² + 2ab + b² to find 61².
  3. 3.Find the value of x² − y² when x = 9 and y = 3.
  4. 4.Use (a − b)² = a² − 2ab + b² to find 89².
  5. 5.Use (a − b)² = a² − 2ab + b² to find 69².
  6. 6.Use a² − b² = (a + b)(a − b) to find 74² − 11².
  7. 7.Find the value of x² + 2xy + y² when x = 4 and y = 2.
  8. 8.Find the value of x² + 2xy + y² when x = 10 and y = 7.
  9. 9.Find the value of x² + 2xy + y² when x = 9 and y = 2.
  10. 10.Use (a + b)² = a² + 2ab + b² to find 25².
  11. 11.Use a² − b² = (a + b)(a − b) to find 84² − 58².
  12. 12.Use (a + b)(a − b) = a² − b² to find 98 × 82.
  13. 13.Use (a + b)² = a² + 2ab + b² to find 31².
  14. 14.Find the value of x² + 2xy + y² when x = 7 and y = 5.
  15. 15.Find the value of x² − 2xy + y² when x = 9 and y = 4.
  16. 16.Use (a − b)² = a² − 2ab + b² to find 38².
  17. 17.Use (a − b)² = a² − 2ab + b² to find 23².
  18. 18.Use (a + b)² = a² + 2ab + b² to find 105².
  19. 19.Use a² − b² = (a + b)(a − b) to find 66² − 30².
  20. 20.If a + b = 6 and ab = 8, what is a² + b²?
  21. 21.Use (a + b)² = a² + 2ab + b² to find 16².
  22. 22.Find the value of x² − y² when x = 8 and y = 1.
  23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
  24. 24.Use (a + b)² = a² + 2ab + b² to find 17².
  25. 25.Find the value of x² − y² when x = 6 and y = 3.
  26. 26.Find the value of x² + 2xy + y² when x = 5 and y = 3.
  27. 27.Use a² − b² = (a + b)(a − b) to find 59² − 5².
  28. 28.Find the value of x² − 2xy + y² when x = 10 and y = 1.
  29. 29.Find the value of x² − 2xy + y² when x = 4 and y = 2.
  30. 30.Find the value of x² − 2xy + y² when x = 4 and y = 1.
  31. 31.Use (a − b)² = a² − 2ab + b² to find 28².
  32. 32.Use (a + b)² = a² + 2ab + b² to find 73².
  33. 33.Use (a + b)² = a² + 2ab + b² to find 29².
  34. 34.Use (a + b)² = a² + 2ab + b² to find 21².
  35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 6.
  36. 36.Use (a − b)² = a² − 2ab + b² to find 31².
  37. 37.If a + b = 14 and ab = 24, what is a² + b²?
  38. 38.Use (a − b)² = a² − 2ab + b² to find 82².
  39. 39.Use (a + b)² = a² + 2ab + b² to find 59².
  40. 40.Use (a + b)² = a² + 2ab + b² to find 24².

Answer key

  1. 1156
  2. 3721
  3. 72
  4. 7921
  5. 4761
  6. 5355
  7. 36
  8. 289
  9. 121
  10. 625
  11. 3692
  12. 8036
  13. 961
  14. 144
  15. 25
  16. 1444
  17. 529
  18. 11025
  19. 3456
  20. 20
  21. 256
  22. 63
  23. 196
  24. 289
  25. 27
  26. 64
  27. 3456
  28. 81
  29. 4
  30. 9
  31. 784
  32. 5329
  33. 841
  34. 441
  35. 256
  36. 961
  37. 148
  38. 6724
  39. 3481
  40. 576

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