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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 24 · 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)(a − b) = a² − b² to find 102 × 98.
  2. 2.Find the value of x² − y² when x = 8 and y = 2.
  3. 3.Use (a − b)² = a² − 2ab + b² to find 24².
  4. 4.Use (a + b)² = a² + 2ab + b² to find 71².
  5. 5.Use a² − b² = (a + b)(a − b) to find 41² − 27².
  6. 6.Use (a + b)² = a² + 2ab + b² to find 56².
  7. 7.Use (a + b)² = a² + 2ab + b² to find 16².
  8. 8.Use (a − b)² = a² − 2ab + b² to find 49².
  9. 9.Find the value of x² − y² when x = 10 and y = 7.
  10. 10.Use (a − b)² = a² − 2ab + b² to find 51².
  11. 11.Use (a + b)² = a² + 2ab + b² to find 66².
  12. 12.Use a² − b² = (a + b)(a − b) to find 20² − 17².
  13. 13.If a + b = 18 and ab = 80, what is a² + b²?
  14. 14.Use (a + b)(a − b) = a² − b² to find 26 × 14.
  15. 15.If a + b = 10 and ab = 16, what is a² + b²?
  16. 16.Use a² − b² = (a + b)(a − b) to find 95² − 5².
  17. 17.Use (a + b)² = a² + 2ab + b² to find 17².
  18. 18.Use (a + b)(a − b) = a² − b² to find 76 × 64.
  19. 19.Use (a − b)² = a² − 2ab + b² to find 66².
  20. 20.Use (a − b)² = a² − 2ab + b² to find 61².
  21. 21.Find the value of x² − y² when x = 8 and y = 5.
  22. 22.Use (a − b)² = a² − 2ab + b² to find 72².
  23. 23.Use (a + b)(a − b) = a² − b² to find 53 × 47.
  24. 24.Use (a − b)² = a² − 2ab + b² to find 26².
  25. 25.Find the value of x² + 2xy + y² when x = 8 and y = 3.
  26. 26.If a + b = 6 and ab = 5, what is a² + b²?
  27. 27.Use (a − b)² = a² − 2ab + b² to find 16².
  28. 28.Use (a + b)² = a² + 2ab + b² to find 29².
  29. 29.Use a² − b² = (a + b)(a − b) to find 28² − 17².
  30. 30.Use (a + b)² = a² + 2ab + b² to find 64².
  31. 31.Find the value of x² − y² when x = 8 and y = 4.
  32. 32.Find the value of x² − y² when x = 4 and y = 2.
  33. 33.Find the value of x² + 2xy + y² when x = 10 and y = 4.
  34. 34.Use (a + b)² = a² + 2ab + b² to find 51².
  35. 35.Find the value of x² − y² when x = 6 and y = 1.
  36. 36.Use a² − b² = (a + b)(a − b) to find 65² − 32².
  37. 37.If a − b = 2 and ab = 8, what is a² + b²?
  38. 38.If a + b = 7 and ab = 6, what is a² + b²?
  39. 39.Find the value of x² − 2xy + y² when x = 7 and y = 6.
  40. 40.Use (a + b)² = a² + 2ab + b² to find 52².

Answer key

  1. 9996
  2. 60
  3. 576
  4. 5041
  5. 952
  6. 3136
  7. 256
  8. 2401
  9. 51
  10. 2601
  11. 4356
  12. 111
  13. 164
  14. 364
  15. 68
  16. 9000
  17. 289
  18. 4864
  19. 4356
  20. 3721
  21. 39
  22. 5184
  23. 2491
  24. 676
  25. 121
  26. 26
  27. 256
  28. 841
  29. 495
  30. 4096
  31. 48
  32. 12
  33. 196
  34. 2601
  35. 35
  36. 3201
  37. 20
  38. 37
  39. 1
  40. 2704

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