Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 665 · 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 − y² when x = 5 and y = 3.
2. 2.Use (a + b)² = a² + 2ab + b² to find 91².
3. 3.Use (a − b)² = a² − 2ab + b² to find 26².
4. 4.Use (a + b)(a − b) = a² − b² to find 41 × 39.
5. 5.Use a² − b² = (a + b)(a − b) to find 30² − 23².
6. 6.Find the value of x² − 2xy + y² when x = 10 and y = 9.
7. 7.Use (a − b)² = a² − 2ab + b² to find 97².
8. 8.If a − b = 9 and ab = 36, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 78².
10. 10.Use (a − b)² = a² − 2ab + b² to find 76².
11. 11.Use (a + b)(a − b) = a² − b² to find 25 × 15.
12. 12.Use a² − b² = (a + b)(a − b) to find 56² − 2².
13. 13.Use (a + b)(a − b) = a² − b² to find 22 × 18.
14. 14.Use (a + b)² = a² + 2ab + b² to find 88².
15. 15.Use (a − b)² = a² − 2ab + b² to find 62².
16. 16.Use (a + b)² = a² + 2ab + b² to find 16².
17. 17.Use a² − b² = (a + b)(a − b) to find 24² − 11².
18. 18.Use a² − b² = (a + b)(a − b) to find 71² − 46².
19. 19.If a + b = 7 and ab = 6, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 91 × 89.
21. 21.Use (a + b)² = a² + 2ab + b² to find 101².
22. 22.Use (a − b)² = a² − 2ab + b² to find 23².
23. 23.Use (a − b)² = a² − 2ab + b² to find 95².
24. 24.If a + b = 14 and ab = 45, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 15².
26. 26.Use a² − b² = (a + b)(a − b) to find 47² − 28².
27. 27.If a − b = 5 and ab = 14, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 68².
29. 29.If a + b = 9 and ab = 18, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 31².
31. 31.Use a² − b² = (a + b)(a − b) to find 45² − 11².
32. 32.Use (a − b)² = a² − 2ab + b² to find 14².
33. 33.If a + b = 17 and ab = 60, what is a² + b²?
34. 34.Find the value of x² − y² when x = 7 and y = 2.
35. 35.Use (a + b)² = a² + 2ab + b² to find 72².
36. 36.Use (a − b)² = a² − 2ab + b² to find 86².
37. 37.Use (a + b)² = a² + 2ab + b² to find 57².
38. 38.Use (a + b)² = a² + 2ab + b² to find 71².
39. 39.If a − b = 2 and ab = 8, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 97² − 44².

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