Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 873 · 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.Use a² − b² = (a + b)(a − b) to find 41² − 15².
2. 2.Use (a + b)² = a² + 2ab + b² to find 96².
3. 3.Use (a + b)² = a² + 2ab + b² to find 76².
4. 4.If a − b = 1 and ab = 6, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 24².
6. 6.Use a² − b² = (a + b)(a − b) to find 52² − 7².
7. 7.Use a² − b² = (a + b)(a − b) to find 21² − 4².
8. 8.Use a² − b² = (a + b)(a − b) to find 42² − 2².
9. 9.Find the value of x² + 2xy + y² when x = 13 and y = 6.
10. 10.Use (a − b)² = a² − 2ab + b² to find 91².
11. 11.Use (a + b)² = a² + 2ab + b² to find 53².
12. 12.Use (a − b)² = a² − 2ab + b² to find 77².
13. 13.Use (a − b)² = a² − 2ab + b² to find 52².
14. 14.Use a² − b² = (a + b)(a − b) to find 80² − 7².
15. 15.Use (a − b)² = a² − 2ab + b² to find 13².
16. 16.Use (a + b)² = a² + 2ab + b² to find 64².
17. 17.Use (a − b)² = a² − 2ab + b² to find 12².
18. 18.Use a² − b² = (a + b)(a − b) to find 29² − 8².
19. 19.Use (a − b)² = a² − 2ab + b² to find 32².
20. 20.Use (a + b)² = a² + 2ab + b² to find 54².
21. 21.Use (a + b)² = a² + 2ab + b² to find 78².
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 6.
23. 23.Use a² − b² = (a + b)(a − b) to find 33² − 11².
24. 24.Use a² − b² = (a + b)(a − b) to find 36² − 2².
25. 25.Use (a + b)² = a² + 2ab + b² to find 62².
26. 26.Use (a + b)² = a² + 2ab + b² to find 107².
27. 27.Use (a + b)² = a² + 2ab + b² to find 104².
28. 28.Use (a + b)(a − b) = a² − b² to find 71 × 69.
29. 29.Use (a − b)² = a² − 2ab + b² to find 43².
30. 30.If a + b = 10 and ab = 21, what is a² + b²?
31. 31.If a + b = 9 and ab = 20, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 108².
33. 33.Use (a + b)² = a² + 2ab + b² to find 59².
34. 34.Use a² − b² = (a + b)(a − b) to find 20² − 2².
35. 35.Use a² − b² = (a + b)(a − b) to find 30² − 8².
36. 36.Use (a + b)(a − b) = a² − b² to find 24 × 16.
37. 37.If a − b = 3 and ab = 40, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 32 × 28.
39. 39.Use (a + b)² = a² + 2ab + b² to find 12².
40. 40.Use a² − b² = (a + b)(a − b) to find 35² − 4².

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