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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 272 · 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 53².
  2. 2.Use (a − b)² = a² − 2ab + b² to find 29².
  3. 3.Find the value of x² − y² when x = 13 and y = 5.
  4. 4.Use (a − b)² = a² − 2ab + b² to find 32².
  5. 5.Find the value of x² + 2xy + y² when x = 4 and y = 1.
  6. 6.Use a² − b² = (a + b)(a − b) to find 59² − 17².
  7. 7.Find the value of x² − 2xy + y² when x = 6 and y = 1.
  8. 8.Use (a − b)² = a² − 2ab + b² to find 84².
  9. 9.If a − b = 2 and ab = 3, what is a² + b²?
  10. 10.Find the value of x² − 2xy + y² when x = 13 and y = 8.
  11. 11.Use a² − b² = (a + b)(a − b) to find 33² − 9².
  12. 12.If a − b = 5 and ab = 14, what is a² + b²?
  13. 13.If a + b = 7 and ab = 10, what is a² + b²?
  14. 14.Find the value of x² − y² when x = 6 and y = 5.
  15. 15.Use a² − b² = (a + b)(a − b) to find 77² − 7².
  16. 16.Use a² − b² = (a + b)(a − b) to find 31² − 22².
  17. 17.Use (a − b)² = a² − 2ab + b² to find 31².
  18. 18.Use (a + b)(a − b) = a² − b² to find 97 × 83.
  19. 19.Use (a + b)² = a² + 2ab + b² to find 34².
  20. 20.Use (a + b)(a − b) = a² − b² to find 67 × 53.
  21. 21.Use (a + b)² = a² + 2ab + b² to find 89².
  22. 22.If a + b = 14 and ab = 33, what is a² + b²?
  23. 23.Use (a − b)² = a² − 2ab + b² to find 96².
  24. 24.Use a² − b² = (a + b)(a − b) to find 44² − 4².
  25. 25.Find the value of x² − 2xy + y² when x = 11 and y = 3.
  26. 26.If a − b = 1 and ab = 2, what is a² + b²?
  27. 27.Find the value of x² − y² when x = 4 and y = 1.
  28. 28.If a + b = 4 and ab = 3, what is a² + b²?
  29. 29.Use (a + b)(a − b) = a² − b² to find 71 × 69.
  30. 30.Use (a + b)² = a² + 2ab + b² to find 12².
  31. 31.Find the value of x² − y² when x = 12 and y = 3.
  32. 32.Use a² − b² = (a + b)(a − b) to find 55² − 32².
  33. 33.If a + b = 20 and ab = 96, what is a² + b²?
  34. 34.Use (a − b)² = a² − 2ab + b² to find 16².
  35. 35.Find the value of x² − 2xy + y² when x = 11 and y = 1.
  36. 36.If a + b = 18 and ab = 77, what is a² + b²?
  37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 1.
  38. 38.Use a² − b² = (a + b)(a − b) to find 71² − 57².
  39. 39.Use (a + b)(a − b) = a² − b² to find 109 × 91.
  40. 40.Use a² − b² = (a + b)(a − b) to find 55² − 28².

Answer key

  1. 2809
  2. 841
  3. 144
  4. 1024
  5. 25
  6. 3192
  7. 25
  8. 7056
  9. 10
  10. 25
  11. 1008
  12. 53
  13. 29
  14. 11
  15. 5880
  16. 477
  17. 961
  18. 8051
  19. 1156
  20. 3551
  21. 7921
  22. 130
  23. 9216
  24. 1920
  25. 64
  26. 5
  27. 15
  28. 10
  29. 4899
  30. 144
  31. 135
  32. 2001
  33. 208
  34. 256
  35. 100
  36. 170
  37. 9
  38. 1792
  39. 9919
  40. 2241

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