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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 787 · 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 31 × 29.
  2. 2.If a + b = 12 and ab = 32, what is a² + b²?
  3. 3.Find the value of x² − 2xy + y² when x = 12 and y = 8.
  4. 4.Use (a + b)² = a² + 2ab + b² to find 81².
  5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
  6. 6.If a + b = 8 and ab = 15, what is a² + b²?
  7. 7.Find the value of x² + 2xy + y² when x = 3 and y = 2.
  8. 8.Use (a + b)(a − b) = a² − b² to find 46 × 34.
  9. 9.Use (a + b)(a − b) = a² − b² to find 73 × 67.
  10. 10.Use (a + b)² = a² + 2ab + b² to find 24².
  11. 11.Use (a + b)² = a² + 2ab + b² to find 71².
  12. 12.Use (a + b)² = a² + 2ab + b² to find 54².
  13. 13.If a − b = 4 and ab = 77, what is a² + b²?
  14. 14.Use (a + b)(a − b) = a² − b² to find 34 × 26.
  15. 15.If a + b = 5 and ab = 6, what is a² + b²?
  16. 16.Use a² − b² = (a + b)(a − b) to find 27² − 23².
  17. 17.Find the value of x² − y² when x = 15 and y = 11.
  18. 18.Use (a + b)² = a² + 2ab + b² to find 12².
  19. 19.Use (a − b)² = a² − 2ab + b² to find 71².
  20. 20.If a + b = 16 and ab = 63, what is a² + b²?
  21. 21.Use (a + b)² = a² + 2ab + b² to find 74².
  22. 22.Use (a + b)² = a² + 2ab + b² to find 17².
  23. 23.If a − b = 2 and ab = 35, what is a² + b²?
  24. 24.If a − b = 1 and ab = 12, what is a² + b²?
  25. 25.Use (a − b)² = a² − 2ab + b² to find 37².
  26. 26.Use (a + b)(a − b) = a² − b² to find 23 × 17.
  27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 7.
  28. 28.Use (a − b)² = a² − 2ab + b² to find 87².
  29. 29.Use (a + b)(a − b) = a² − b² to find 78 × 62.
  30. 30.Use (a + b)² = a² + 2ab + b² to find 73².
  31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
  32. 32.If a + b = 14 and ab = 48, what is a² + b²?
  33. 33.Find the value of x² − y² when x = 8 and y = 3.
  34. 34.Use (a − b)² = a² − 2ab + b² to find 11².
  35. 35.Use (a − b)² = a² − 2ab + b² to find 63².
  36. 36.Use (a + b)² = a² + 2ab + b² to find 91².
  37. 37.Use a² − b² = (a + b)(a − b) to find 77² − 63².
  38. 38.Use (a + b)² = a² + 2ab + b² to find 19².
  39. 39.If a + b = 6 and ab = 8, what is a² + b²?
  40. 40.Find the value of x² + 2xy + y² when x = 14 and y = 6.

Answer key

  1. 899
  2. 80
  3. 16
  4. 6561
  5. 3249
  6. 34
  7. 25
  8. 1564
  9. 4891
  10. 576
  11. 5041
  12. 2916
  13. 170
  14. 884
  15. 13
  16. 200
  17. 104
  18. 144
  19. 5041
  20. 130
  21. 5476
  22. 289
  23. 74
  24. 25
  25. 1369
  26. 391
  27. 256
  28. 7569
  29. 4836
  30. 5329
  31. 8464
  32. 100
  33. 55
  34. 121
  35. 3969
  36. 8281
  37. 1960
  38. 361
  39. 20
  40. 400

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