Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 501 · 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 (a − b)² = a² − 2ab + b² to find 64².
2. 2.Use (a + b)² = a² + 2ab + b² to find 36².
3. 3.Use (a + b)(a − b) = a² − b² to find 103 × 97.
4. 4.Use (a − b)² = a² − 2ab + b² to find 23².
5. 5.Find the value of x² − 2xy + y² when x = 5 and y = 3.
6. 6.If a − b = 1 and ab = 6, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 42 × 38.
8. 8.Use (a + b)(a − b) = a² − b² to find 104 × 96.
9. 9.Use (a + b)² = a² + 2ab + b² to find 43².
10. 10.Use a² − b² = (a + b)(a − b) to find 56² − 26².
11. 11.Use (a + b)(a − b) = a² − b² to find 81 × 79.
12. 12.Use (a + b)(a − b) = a² − b² to find 72 × 68.
13. 13.Use (a + b)² = a² + 2ab + b² to find 56².
14. 14.Use (a − b)² = a² − 2ab + b² to find 42².
15. 15.Use (a + b)² = a² + 2ab + b² to find 85².
16. 16.Use a² − b² = (a + b)(a − b) to find 95² − 30².
17. 17.Use (a − b)² = a² − 2ab + b² to find 26².
18. 18.Use (a + b)(a − b) = a² − b² to find 46 × 34.
19. 19.Use (a + b)(a − b) = a² − b² to find 95 × 85.
20. 20.Use (a − b)² = a² − 2ab + b² to find 71².
21. 21.Use a² − b² = (a + b)(a − b) to find 29² − 2².
22. 22.Use a² − b² = (a + b)(a − b) to find 22² − 3².
23. 23.Use a² − b² = (a + b)(a − b) to find 63² − 13².
24. 24.If a + b = 4 and ab = 3, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 69².
26. 26.Use (a + b)² = a² + 2ab + b² to find 18².
27. 27.Use a² − b² = (a + b)(a − b) to find 97² − 60².
28. 28.Use a² − b² = (a + b)(a − b) to find 80² − 73².
29. 29.Use a² − b² = (a + b)(a − b) to find 69² − 19².
30. 30.Use (a − b)² = a² − 2ab + b² to find 41².
31. 31.Use (a − b)² = a² − 2ab + b² to find 83².
32. 32.Use (a + b)(a − b) = a² − b² to find 85 × 75.
33. 33.Use (a + b)(a − b) = a² − b² to find 45 × 35.
34. 34.If a − b = 4 and ab = 5, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 52².
36. 36.Find the value of x² − y² when x = 5 and y = 2.
37. 37.Use (a − b)² = a² − 2ab + b² to find 44².
38. 38.Use (a − b)² = a² − 2ab + b² to find 87².
39. 39.Use a² − b² = (a + b)(a − b) to find 31² − 12².
40. 40.Use (a + b)² = a² + 2ab + b² to find 55².

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