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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 246 · 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 24².
  2. 2.If a − b = 4 and ab = 45, what is a² + b²?
  3. 3.Use a² − b² = (a + b)(a − b) to find 98² − 57².
  4. 4.Use (a + b)(a − b) = a² − b² to find 63 × 57.
  5. 5.Use (a + b)(a − b) = a² − b² to find 81 × 79.
  6. 6.Use a² − b² = (a + b)(a − b) to find 27² − 23².
  7. 7.Find the value of x² − 2xy + y² when x = 8 and y = 7.
  8. 8.Use (a − b)² = a² − 2ab + b² to find 61².
  9. 9.Find the value of x² − y² when x = 11 and y = 9.
  10. 10.Find the value of x² − 2xy + y² when x = 14 and y = 3.
  11. 11.If a + b = 8 and ab = 7, what is a² + b²?
  12. 12.Use (a − b)² = a² − 2ab + b² to find 53².
  13. 13.If a − b = 2 and ab = 63, what is a² + b²?
  14. 14.Find the value of x² − 2xy + y² when x = 6 and y = 2.
  15. 15.Use (a + b)² = a² + 2ab + b² to find 41².
  16. 16.Use a² − b² = (a + b)(a − b) to find 72² − 21².
  17. 17.Use a² − b² = (a + b)(a − b) to find 25² − 22².
  18. 18.Use (a + b)² = a² + 2ab + b² to find 19².
  19. 19.Find the value of x² − y² when x = 11 and y = 8.
  20. 20.Use (a + b)² = a² + 2ab + b² to find 43².
  21. 21.Use (a + b)² = a² + 2ab + b² to find 46².
  22. 22.Find the value of x² + 2xy + y² when x = 14 and y = 6.
  23. 23.Use (a − b)² = a² − 2ab + b² to find 38².
  24. 24.If a − b = 8 and ab = 9, what is a² + b²?
  25. 25.Use (a − b)² = a² − 2ab + b² to find 19².
  26. 26.Use (a + b)² = a² + 2ab + b² to find 15².
  27. 27.Use (a + b)² = a² + 2ab + b² to find 108².
  28. 28.Find the value of x² − y² when x = 13 and y = 5.
  29. 29.Use a² − b² = (a + b)(a − b) to find 92² − 14².
  30. 30.Use (a + b)(a − b) = a² − b² to find 21 × 19.
  31. 31.Use a² − b² = (a + b)(a − b) to find 25² − 7².
  32. 32.Use a² − b² = (a + b)(a − b) to find 76² − 60².
  33. 33.Use (a − b)² = a² − 2ab + b² to find 14².
  34. 34.Find the value of x² + 2xy + y² when x = 5 and y = 3.
  35. 35.If a + b = 23 and ab = 132, what is a² + b²?
  36. 36.Use (a + b)² = a² + 2ab + b² to find 11².
  37. 37.Use (a + b)(a − b) = a² − b² to find 51 × 49.
  38. 38.Use (a + b)² = a² + 2ab + b² to find 27².
  39. 39.If a + b = 14 and ab = 33, what is a² + b²?
  40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 2.

Answer key

  1. 576
  2. 106
  3. 6355
  4. 3591
  5. 6399
  6. 200
  7. 1
  8. 3721
  9. 40
  10. 121
  11. 50
  12. 2809
  13. 130
  14. 16
  15. 1681
  16. 4743
  17. 141
  18. 361
  19. 57
  20. 1849
  21. 2116
  22. 400
  23. 1444
  24. 82
  25. 361
  26. 225
  27. 11664
  28. 144
  29. 8268
  30. 399
  31. 576
  32. 2176
  33. 196
  34. 64
  35. 265
  36. 121
  37. 2499
  38. 729
  39. 130
  40. 1

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