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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 956 · 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)² = a² − 2ab + b² to find 99².
  2. 2.Use a² − b² = (a + b)(a − b) to find 55² − 47².
  3. 3.Use a² − b² = (a + b)(a − b) to find 32² − 1².
  4. 4.Use (a − b)² = a² − 2ab + b² to find 13².
  5. 5.Use (a + b)(a − b) = a² − b² to find 49 × 31.
  6. 6.Find the value of x² − y² when x = 13 and y = 7.
  7. 7.Use (a − b)² = a² − 2ab + b² to find 29².
  8. 8.If a − b = 2 and ab = 3, what is a² + b²?
  9. 9.Use (a − b)² = a² − 2ab + b² to find 44².
  10. 10.Use a² − b² = (a + b)(a − b) to find 51² − 12².
  11. 11.Use (a − b)² = a² − 2ab + b² to find 57².
  12. 12.Use (a + b)² = a² + 2ab + b² to find 73².
  13. 13.If a + b = 13 and ab = 36, what is a² + b²?
  14. 14.If a − b = 7 and ab = 18, what is a² + b²?
  15. 15.Use (a − b)² = a² − 2ab + b² to find 28².
  16. 16.Find the value of x² − y² when x = 5 and y = 3.
  17. 17.Use (a + b)(a − b) = a² − b² to find 27 × 13.
  18. 18.Use (a + b)² = a² + 2ab + b² to find 23².
  19. 19.Use (a − b)² = a² − 2ab + b² to find 84².
  20. 20.Use (a + b)² = a² + 2ab + b² to find 42².
  21. 21.Use (a + b)² = a² + 2ab + b² to find 58².
  22. 22.Use (a − b)² = a² − 2ab + b² to find 68².
  23. 23.Use (a + b)(a − b) = a² − b² to find 62 × 58.
  24. 24.Use (a + b)² = a² + 2ab + b² to find 71².
  25. 25.Use (a − b)² = a² − 2ab + b² to find 98².
  26. 26.Find the value of x² − y² when x = 5 and y = 1.
  27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 3.
  28. 28.Find the value of x² + 2xy + y² when x = 3 and y = 1.
  29. 29.Use (a + b)² = a² + 2ab + b² to find 106².
  30. 30.If a + b = 5 and ab = 6, what is a² + b²?
  31. 31.Use (a + b)² = a² + 2ab + b² to find 14².
  32. 32.Use (a − b)² = a² − 2ab + b² to find 45².
  33. 33.If a + b = 8 and ab = 7, what is a² + b²?
  34. 34.Find the value of x² − 2xy + y² when x = 11 and y = 7.
  35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 1.
  36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 1.
  37. 37.Use (a + b)² = a² + 2ab + b² to find 95².
  38. 38.Use a² − b² = (a + b)(a − b) to find 78² − 18².
  39. 39.If a + b = 7 and ab = 6, what is a² + b²?
  40. 40.If a + b = 7 and ab = 12, what is a² + b²?

Answer key

  1. 9801
  2. 816
  3. 1023
  4. 169
  5. 1519
  6. 120
  7. 841
  8. 10
  9. 1936
  10. 2457
  11. 3249
  12. 5329
  13. 97
  14. 85
  15. 784
  16. 16
  17. 351
  18. 529
  19. 7056
  20. 1764
  21. 3364
  22. 4624
  23. 3596
  24. 5041
  25. 9604
  26. 24
  27. 64
  28. 16
  29. 11236
  30. 13
  31. 196
  32. 2025
  33. 50
  34. 16
  35. 100
  36. 36
  37. 9025
  38. 5760
  39. 37
  40. 25

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