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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 183 · 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 + 2xy + y² when x = 6 and y = 2.
  2. 2.If a − b = 1 and ab = 110, what is a² + b²?
  3. 3.Use (a + b)² = a² + 2ab + b² to find 61².
  4. 4.Use (a + b)² = a² + 2ab + b² to find 11².
  5. 5.Find the value of x² − 2xy + y² when x = 8 and y = 4.
  6. 6.Use (a − b)² = a² − 2ab + b² to find 96².
  7. 7.Use (a + b)² = a² + 2ab + b² to find 77².
  8. 8.Use (a + b)(a − b) = a² − b² to find 61 × 59.
  9. 9.Use (a − b)² = a² − 2ab + b² to find 91².
  10. 10.Use (a + b)(a − b) = a² − b² to find 99 × 81.
  11. 11.If a − b = 6 and ab = 7, what is a² + b²?
  12. 12.If a − b = 6 and ab = 72, what is a² + b²?
  13. 13.If a − b = 1 and ab = 90, what is a² + b²?
  14. 14.If a − b = 1 and ab = 6, what is a² + b²?
  15. 15.If a − b = 2 and ab = 3, what is a² + b²?
  16. 16.Find the value of x² − y² when x = 11 and y = 2.
  17. 17.If a − b = 2 and ab = 80, what is a² + b²?
  18. 18.Find the value of x² − y² when x = 13 and y = 9.
  19. 19.If a + b = 5 and ab = 4, what is a² + b²?
  20. 20.Use (a + b)² = a² + 2ab + b² to find 67².
  21. 21.Use (a − b)² = a² − 2ab + b² to find 19².
  22. 22.Use a² − b² = (a + b)(a − b) to find 82² − 15².
  23. 23.Use (a − b)² = a² − 2ab + b² to find 77².
  24. 24.If a − b = 1 and ab = 30, what is a² + b²?
  25. 25.Find the value of x² − y² when x = 5 and y = 2.
  26. 26.Use (a + b)² = a² + 2ab + b² to find 21².
  27. 27.Use (a + b)² = a² + 2ab + b² to find 84².
  28. 28.Use (a − b)² = a² − 2ab + b² to find 16².
  29. 29.Use (a − b)² = a² − 2ab + b² to find 32².
  30. 30.Find the value of x² − y² when x = 9 and y = 5.
  31. 31.If a + b = 3 and ab = 2, what is a² + b²?
  32. 32.Use (a + b)(a − b) = a² − b² to find 92 × 88.
  33. 33.Use (a + b)(a − b) = a² − b² to find 63 × 57.
  34. 34.If a − b = 3 and ab = 4, what is a² + b²?
  35. 35.Use (a − b)² = a² − 2ab + b² to find 76².
  36. 36.Use (a − b)² = a² − 2ab + b² to find 27².
  37. 37.Use a² − b² = (a + b)(a − b) to find 80² − 46².
  38. 38.If a − b = 6 and ab = 16, what is a² + b²?
  39. 39.If a − b = 1 and ab = 72, what is a² + b²?
  40. 40.Use (a + b)² = a² + 2ab + b² to find 74².

Answer key

  1. 64
  2. 221
  3. 3721
  4. 121
  5. 16
  6. 9216
  7. 5929
  8. 3599
  9. 8281
  10. 8019
  11. 50
  12. 180
  13. 181
  14. 13
  15. 10
  16. 117
  17. 164
  18. 88
  19. 17
  20. 4489
  21. 361
  22. 6499
  23. 5929
  24. 61
  25. 21
  26. 441
  27. 7056
  28. 256
  29. 1024
  30. 56
  31. 5
  32. 8096
  33. 3591
  34. 17
  35. 5776
  36. 729
  37. 4284
  38. 68
  39. 145
  40. 5476

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