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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 976 · 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.If a − b = 8 and ab = 48, what is a² + b²?
  2. 2.Use a² − b² = (a + b)(a − b) to find 73² − 50².
  3. 3.Find the value of x² + 2xy + y² when x = 7 and y = 2.
  4. 4.If a − b = 1 and ab = 132, what is a² + b²?
  5. 5.Use (a − b)² = a² − 2ab + b² to find 66².
  6. 6.Use (a + b)² = a² + 2ab + b² to find 44².
  7. 7.Find the value of x² + 2xy + y² when x = 7 and y = 1.
  8. 8.Find the value of x² − 2xy + y² when x = 12 and y = 1.
  9. 9.Use (a + b)(a − b) = a² − b² to find 67 × 53.
  10. 10.Use (a + b)² = a² + 2ab + b² to find 46².
  11. 11.If a + b = 16 and ab = 48, what is a² + b²?
  12. 12.Find the value of x² + 2xy + y² when x = 6 and y = 1.
  13. 13.If a + b = 14 and ab = 48, what is a² + b²?
  14. 14.Use (a − b)² = a² − 2ab + b² to find 12².
  15. 15.Use (a + b)(a − b) = a² − b² to find 87 × 73.
  16. 16.Use a² − b² = (a + b)(a − b) to find 68² − 2².
  17. 17.If a − b = 1 and ab = 12, what is a² + b²?
  18. 18.Use (a − b)² = a² − 2ab + b² to find 17².
  19. 19.Use (a + b)² = a² + 2ab + b² to find 41².
  20. 20.Use (a + b)(a − b) = a² − b² to find 32 × 28.
  21. 21.Use (a − b)² = a² − 2ab + b² to find 61².
  22. 22.If a + b = 11 and ab = 30, what is a² + b²?
  23. 23.If a + b = 7 and ab = 6, what is a² + b²?
  24. 24.Use (a + b)(a − b) = a² − b² to find 101 × 99.
  25. 25.Use a² − b² = (a + b)(a − b) to find 91² − 77².
  26. 26.If a − b = 8 and ab = 33, what is a² + b²?
  27. 27.Use (a − b)² = a² − 2ab + b² to find 53².
  28. 28.Use (a − b)² = a² − 2ab + b² to find 84².
  29. 29.Find the value of x² − y² when x = 9 and y = 3.
  30. 30.Use (a + b)² = a² + 2ab + b² to find 32².
  31. 31.Use a² − b² = (a + b)(a − b) to find 31² − 14².
  32. 32.If a + b = 15 and ab = 36, what is a² + b²?
  33. 33.Find the value of x² + 2xy + y² when x = 14 and y = 3.
  34. 34.Use (a + b)² = a² + 2ab + b² to find 75².
  35. 35.Use a² − b² = (a + b)(a − b) to find 48² − 15².
  36. 36.Find the value of x² − y² when x = 6 and y = 1.
  37. 37.If a + b = 8 and ab = 12, what is a² + b²?
  38. 38.Use (a − b)² = a² − 2ab + b² to find 91².
  39. 39.If a + b = 5 and ab = 4, what is a² + b²?
  40. 40.Use (a + b)² = a² + 2ab + b² to find 92².

Answer key

  1. 160
  2. 2829
  3. 81
  4. 265
  5. 4356
  6. 1936
  7. 64
  8. 121
  9. 3551
  10. 2116
  11. 160
  12. 49
  13. 100
  14. 144
  15. 6351
  16. 4620
  17. 25
  18. 289
  19. 1681
  20. 896
  21. 3721
  22. 61
  23. 37
  24. 9999
  25. 2352
  26. 130
  27. 2809
  28. 7056
  29. 72
  30. 1024
  31. 765
  32. 153
  33. 289
  34. 5625
  35. 2079
  36. 35
  37. 40
  38. 8281
  39. 17
  40. 8464

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