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Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 299 · 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 43 × 37.
  2. 2.Use (a + b)² = a² + 2ab + b² to find 73².
  3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
  4. 4.Use a² − b² = (a + b)(a − b) to find 88² − 47².
  5. 5.If a + b = 5 and ab = 6, what is a² + b²?
  6. 6.Use (a + b)(a − b) = a² − b² to find 72 × 68.
  7. 7.Find the value of x² − 2xy + y² when x = 5 and y = 2.
  8. 8.Use (a + b)² = a² + 2ab + b² to find 89².
  9. 9.Use (a − b)² = a² − 2ab + b² to find 32².
  10. 10.Use (a + b)² = a² + 2ab + b² to find 44².
  11. 11.Find the value of x² − 2xy + y² when x = 8 and y = 2.
  12. 12.Use a² − b² = (a + b)(a − b) to find 77² − 54².
  13. 13.Use a² − b² = (a + b)(a − b) to find 48² − 28².
  14. 14.If a − b = 3 and ab = 54, what is a² + b²?
  15. 15.Find the value of x² − y² when x = 6 and y = 3.
  16. 16.Use (a − b)² = a² − 2ab + b² to find 95².
  17. 17.Find the value of x² + 2xy + y² when x = 9 and y = 1.
  18. 18.If a + b = 7 and ab = 10, what is a² + b²?
  19. 19.Find the value of x² − y² when x = 6 and y = 1.
  20. 20.Use (a + b)² = a² + 2ab + b² to find 54².
  21. 21.Use (a + b)² = a² + 2ab + b² to find 79².
  22. 22.Use (a − b)² = a² − 2ab + b² to find 38².
  23. 23.If a + b = 3 and ab = 2, what is a² + b²?
  24. 24.If a + b = 10 and ab = 16, what is a² + b²?
  25. 25.If a − b = 5 and ab = 6, what is a² + b²?
  26. 26.Use (a − b)² = a² − 2ab + b² to find 71².
  27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 1.
  28. 28.Use (a + b)² = a² + 2ab + b² to find 86².
  29. 29.If a − b = 1 and ab = 2, what is a² + b²?
  30. 30.Use a² − b² = (a + b)(a − b) to find 29² − 16².
  31. 31.Use (a + b)(a − b) = a² − b² to find 62 × 58.
  32. 32.Use (a + b)² = a² + 2ab + b² to find 23².
  33. 33.Use (a + b)² = a² + 2ab + b² to find 36².
  34. 34.Use (a + b)² = a² + 2ab + b² to find 108².
  35. 35.If a − b = 1 and ab = 12, what is a² + b²?
  36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
  37. 37.Use (a + b)² = a² + 2ab + b² to find 49².
  38. 38.Find the value of x² + 2xy + y² when x = 5 and y = 2.
  39. 39.Use (a + b)² = a² + 2ab + b² to find 31².
  40. 40.Use (a + b)² = a² + 2ab + b² to find 19².

Answer key

  1. 1591
  2. 5329
  3. 3025
  4. 5535
  5. 13
  6. 4896
  7. 9
  8. 7921
  9. 1024
  10. 1936
  11. 36
  12. 3013
  13. 1520
  14. 117
  15. 27
  16. 9025
  17. 100
  18. 29
  19. 35
  20. 2916
  21. 6241
  22. 1444
  23. 5
  24. 68
  25. 37
  26. 5041
  27. 25
  28. 7396
  29. 5
  30. 585
  31. 3596
  32. 529
  33. 1296
  34. 11664
  35. 25
  36. 169
  37. 2401
  38. 49
  39. 961
  40. 361

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