Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 412 · 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 61².
2. 2.Use (a + b)² = a² + 2ab + b² to find 14².
3. 3.Use a² − b² = (a + b)(a − b) to find 49² − 26².
4. 4.Use (a + b)² = a² + 2ab + b² to find 49².
5. 5.Use (a − b)² = a² − 2ab + b² to find 12².
6. 6.Use a² − b² = (a + b)(a − b) to find 20² − 13².
7. 7.Use (a − b)² = a² − 2ab + b² to find 29².
8. 8.If a + b = 4 and ab = 3, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 52 × 48.
10. 10.Use a² − b² = (a + b)(a − b) to find 23² − 11².
11. 11.Use a² − b² = (a + b)(a − b) to find 36² − 13².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 66².
14. 14.Find the value of x² + 2xy + y² when x = 13 and y = 9.
15. 15.If a + b = 13 and ab = 22, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 49².
17. 17.Use a² − b² = (a + b)(a − b) to find 63² − 24².
18. 18.Use (a − b)² = a² − 2ab + b² to find 75².
19. 19.Use (a + b)² = a² + 2ab + b² to find 42².
20. 20.Use (a − b)² = a² − 2ab + b² to find 18².
21. 21.Use (a + b)(a − b) = a² − b² to find 77 × 63.
22. 22.Use (a − b)² = a² − 2ab + b² to find 31².
23. 23.Find the value of x² + 2xy + y² when x = 6 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 81².
25. 25.Find the value of x² − 2xy + y² when x = 6 and y = 2.
26. 26.Use (a + b)² = a² + 2ab + b² to find 35².
27. 27.Use (a + b)² = a² + 2ab + b² to find 69².
28. 28.Use (a − b)² = a² − 2ab + b² to find 17².
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 2.
30. 30.Use (a + b)(a − b) = a² − b² to find 55 × 45.
31. 31.Find the value of x² − y² when x = 9 and y = 5.
32. 32.Use (a − b)² = a² − 2ab + b² to find 62².
33. 33.If a − b = 4 and ab = 12, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 10 and y = 9.
35. 35.Find the value of x² − y² when x = 9 and y = 2.
36. 36.If a − b = 2 and ab = 8, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 88².
38. 38.Use (a − b)² = a² − 2ab + b² to find 96².
39. 39.Find the value of x² − 2xy + y² when x = 12 and y = 1.
40. 40.If a − b = 3 and ab = 18, what is a² + b²?

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