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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 374 · 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 36².
  2. 2.If a + b = 6 and ab = 5, what is a² + b²?
  3. 3.Find the value of x² − y² when x = 7 and y = 4.
  4. 4.Find the value of x² − y² when x = 9 and y = 5.
  5. 5.Use a² − b² = (a + b)(a − b) to find 81² − 60².
  6. 6.Use (a − b)² = a² − 2ab + b² to find 34².
  7. 7.Use (a − b)² = a² − 2ab + b² to find 63².
  8. 8.Use (a − b)² = a² − 2ab + b² to find 35².
  9. 9.Use (a − b)² = a² − 2ab + b² to find 74².
  10. 10.Use a² − b² = (a + b)(a − b) to find 52² − 35².
  11. 11.If a + b = 15 and ab = 44, what is a² + b²?
  12. 12.Use (a + b)(a − b) = a² − b² to find 45 × 35.
  13. 13.Find the value of x² − 2xy + y² when x = 3 and y = 2.
  14. 14.Find the value of x² − y² when x = 7 and y = 2.
  15. 15.Use a² − b² = (a + b)(a − b) to find 82² − 16².
  16. 16.Find the value of x² − y² when x = 9 and y = 8.
  17. 17.Use (a − b)² = a² − 2ab + b² to find 27².
  18. 18.Use a² − b² = (a + b)(a − b) to find 39² − 8².
  19. 19.Find the value of x² + 2xy + y² when x = 10 and y = 5.
  20. 20.Use (a + b)² = a² + 2ab + b² to find 35².
  21. 21.Use (a − b)² = a² − 2ab + b² to find 29².
  22. 22.Find the value of x² − y² when x = 13 and y = 7.
  23. 23.Use (a − b)² = a² − 2ab + b² to find 46².
  24. 24.Use a² − b² = (a + b)(a − b) to find 35² − 6².
  25. 25.If a − b = 3 and ab = 40, what is a² + b²?
  26. 26.Find the value of x² − 2xy + y² when x = 3 and y = 1.
  27. 27.Use (a + b)(a − b) = a² − b² to find 44 × 36.
  28. 28.Use (a − b)² = a² − 2ab + b² to find 32².
  29. 29.Find the value of x² − y² when x = 8 and y = 5.
  30. 30.Find the value of x² + 2xy + y² when x = 9 and y = 7.
  31. 31.Use a² − b² = (a + b)(a − b) to find 43² − 33².
  32. 32.Use (a + b)² = a² + 2ab + b² to find 55².
  33. 33.Use a² − b² = (a + b)(a − b) to find 43² − 13².
  34. 34.Use (a + b)(a − b) = a² − b² to find 71 × 69.
  35. 35.Use (a + b)(a − b) = a² − b² to find 93 × 87.
  36. 36.Use (a + b)(a − b) = a² − b² to find 69 × 51.
  37. 37.Use a² − b² = (a + b)(a − b) to find 76² − 8².
  38. 38.If a − b = 1 and ab = 2, what is a² + b²?
  39. 39.If a − b = 5 and ab = 6, what is a² + b²?
  40. 40.Use (a + b)² = a² + 2ab + b² to find 97².

Answer key

  1. 1296
  2. 26
  3. 33
  4. 56
  5. 2961
  6. 1156
  7. 3969
  8. 1225
  9. 5476
  10. 1479
  11. 137
  12. 1575
  13. 1
  14. 45
  15. 6468
  16. 17
  17. 729
  18. 1457
  19. 225
  20. 1225
  21. 841
  22. 120
  23. 2116
  24. 1189
  25. 89
  26. 4
  27. 1584
  28. 1024
  29. 39
  30. 256
  31. 760
  32. 3025
  33. 1680
  34. 4899
  35. 8091
  36. 3519
  37. 5712
  38. 5
  39. 37
  40. 9409

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