Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 127 · 40 sums

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.

1. 1.Find the value of x² − 2xy + y² when x = 9 and y = 7.
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 85².
4. 4.Use (a − b)² = a² − 2ab + b² to find 64².
5. 5.Use a² − b² = (a + b)(a − b) to find 41² − 4².
6. 6.Use a² − b² = (a + b)(a − b) to find 90² − 83².
7. 7.Use (a + b)(a − b) = a² − b² to find 37 × 23.
8. 8.If a − b = 7 and ab = 8, what is a² + b²?
9. 9.If a + b = 10 and ab = 21, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 38² − 16².
11. 11.Use (a + b)(a − b) = a² − b² to find 77 × 63.
12. 12.Use (a + b)(a − b) = a² − b² to find 82 × 78.
13. 13.Find the value of x² − y² when x = 7 and y = 5.
14. 14.Use (a + b)² = a² + 2ab + b² to find 35².
15. 15.Use (a + b)² = a² + 2ab + b² to find 92².
16. 16.Use (a + b)² = a² + 2ab + b² to find 53².
17. 17.Use a² − b² = (a + b)(a − b) to find 71² − 38².
18. 18.Find the value of x² − 2xy + y² when x = 12 and y = 10.
19. 19.Use (a − b)² = a² − 2ab + b² to find 59².
20. 20.Use (a + b)² = a² + 2ab + b² to find 103².
21. 21.Use (a − b)² = a² − 2ab + b² to find 23².
22. 22.Use a² − b² = (a + b)(a − b) to find 99² − 1².
23. 23.Use a² − b² = (a + b)(a − b) to find 42² − 11².
24. 24.Use (a + b)(a − b) = a² − b² to find 103 × 97.
25. 25.Use a² − b² = (a + b)(a − b) to find 42² − 35².
26. 26.Find the value of x² + 2xy + y² when x = 4 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 82².
28. 28.Find the value of x² − 2xy + y² when x = 8 and y = 5.
29. 29.Use (a + b)² = a² + 2ab + b² to find 76².
30. 30.Use (a + b)² = a² + 2ab + b² to find 75².
31. 31.Find the value of x² − y² when x = 10 and y = 2.
32. 32.Use a² − b² = (a + b)(a − b) to find 62² − 26².
33. 33.Use (a + b)² = a² + 2ab + b² to find 71².
34. 34.Find the value of x² − y² when x = 12 and y = 11.
35. 35.Use (a + b)² = a² + 2ab + b² to find 22².
36. 36.Use a² − b² = (a + b)(a − b) to find 86² − 54².
37. 37.If a − b = 1 and ab = 2, what is a² + b²?
38. 38.Find the value of x² − y² when x = 10 and y = 5.
39. 39.Find the value of x² − 2xy + y² when x = 3 and y = 1.
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 2.

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