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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 411 · 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 77² − 15².
  2. 2.Use (a − b)² = a² − 2ab + b² to find 47².
  3. 3.If a + b = 10 and ab = 9, what is a² + b²?
  4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 9.
  5. 5.If a − b = 4 and ab = 5, what is a² + b²?
  6. 6.Use (a − b)² = a² − 2ab + b² to find 34².
  7. 7.If a − b = 10 and ab = 24, what is a² + b²?
  8. 8.Use (a − b)² = a² − 2ab + b² to find 38².
  9. 9.If a − b = 1 and ab = 2, what is a² + b²?
  10. 10.If a + b = 8 and ab = 15, what is a² + b²?
  11. 11.Find the value of x² − y² when x = 9 and y = 7.
  12. 12.Use (a + b)² = a² + 2ab + b² to find 106².
  13. 13.Use (a + b)(a − b) = a² − b² to find 99 × 81.
  14. 14.Use (a + b)² = a² + 2ab + b² to find 22².
  15. 15.Find the value of x² + 2xy + y² when x = 4 and y = 1.
  16. 16.If a + b = 14 and ab = 48, what is a² + b²?
  17. 17.Use (a + b)² = a² + 2ab + b² to find 33².
  18. 18.Use a² − b² = (a + b)(a − b) to find 37² − 23².
  19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 8.
  20. 20.Use (a + b)² = a² + 2ab + b² to find 53².
  21. 21.Use a² − b² = (a + b)(a − b) to find 77² − 33².
  22. 22.Find the value of x² + 2xy + y² when x = 3 and y = 1.
  23. 23.Use (a − b)² = a² − 2ab + b² to find 33².
  24. 24.Use a² − b² = (a + b)(a − b) to find 97² − 88².
  25. 25.Use (a + b)² = a² + 2ab + b² to find 61².
  26. 26.Use (a + b)(a − b) = a² − b² to find 24 × 16.
  27. 27.Use a² − b² = (a + b)(a − b) to find 78² − 57².
  28. 28.If a + b = 4 and ab = 3, what is a² + b²?
  29. 29.If a + b = 16 and ab = 55, what is a² + b²?
  30. 30.Find the value of x² − y² when x = 10 and y = 5.
  31. 31.Find the value of x² + 2xy + y² when x = 15 and y = 3.
  32. 32.Use (a + b)² = a² + 2ab + b² to find 94².
  33. 33.If a + b = 8 and ab = 12, what is a² + b²?
  34. 34.Find the value of x² − y² when x = 5 and y = 4.
  35. 35.Use (a + b)(a − b) = a² − b² to find 62 × 58.
  36. 36.Use a² − b² = (a + b)(a − b) to find 75² − 37².
  37. 37.Use (a + b)² = a² + 2ab + b² to find 19².
  38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 10.
  39. 39.Use (a − b)² = a² − 2ab + b² to find 21².
  40. 40.Find the value of x² − y² when x = 8 and y = 7.

Answer key

  1. 5704
  2. 2209
  3. 82
  4. 484
  5. 26
  6. 1156
  7. 148
  8. 1444
  9. 5
  10. 34
  11. 32
  12. 11236
  13. 8019
  14. 484
  15. 25
  16. 100
  17. 1089
  18. 840
  19. 289
  20. 2809
  21. 4840
  22. 16
  23. 1089
  24. 1665
  25. 3721
  26. 384
  27. 2835
  28. 10
  29. 146
  30. 75
  31. 324
  32. 8836
  33. 40
  34. 9
  35. 3596
  36. 4256
  37. 361
  38. 25
  39. 441
  40. 15

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