Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 825 · 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 28².
2. 2.Use (a − b)² = a² − 2ab + b² to find 78².
3. 3.Find the value of x² − 2xy + y² when x = 12 and y = 7.
4. 4.Use a² − b² = (a + b)(a − b) to find 56² − 38².
5. 5.Use (a − b)² = a² − 2ab + b² to find 69².
6. 6.If a + b = 7 and ab = 10, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 42².
8. 8.Use (a + b)² = a² + 2ab + b² to find 16².
9. 9.If a − b = 5 and ab = 36, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 76².
11. 11.Use (a + b)² = a² + 2ab + b² to find 89².
12. 12.Use (a + b)(a − b) = a² − b² to find 51 × 49.
13. 13.Find the value of x² + 2xy + y² when x = 10 and y = 9.
14. 14.Use a² − b² = (a + b)(a − b) to find 37² − 5².
15. 15.If a + b = 13 and ab = 12, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 98².
17. 17.Use (a − b)² = a² − 2ab + b² to find 88².
18. 18.If a − b = 5 and ab = 14, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 73² − 37².
20. 20.If a − b = 6 and ab = 40, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 55².
22. 22.Find the value of x² − y² when x = 6 and y = 5.
23. 23.Use (a + b)(a − b) = a² − b² to find 91 × 89.
24. 24.Use a² − b² = (a + b)(a − b) to find 54² − 10².
25. 25.Use a² − b² = (a + b)(a − b) to find 26² − 8².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 99².
28. 28.Use (a + b)² = a² + 2ab + b² to find 28².
29. 29.Find the value of x² − 2xy + y² when x = 10 and y = 3.
30. 30.Use (a − b)² = a² − 2ab + b² to find 27².
31. 31.Use (a − b)² = a² − 2ab + b² to find 83².
32. 32.Use (a + b)² = a² + 2ab + b² to find 99².
33. 33.Use (a + b)² = a² + 2ab + b² to find 88².
34. 34.Use (a + b)(a − b) = a² − b² to find 24 × 16.
35. 35.Use (a + b)(a − b) = a² − b² to find 84 × 76.
36. 36.Use (a − b)² = a² − 2ab + b² to find 96².
37. 37.Use a² − b² = (a + b)(a − b) to find 53² − 21².
38. 38.If a + b = 7 and ab = 12, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 56².
40. 40.If a − b = 4 and ab = 12, what is a² + b²?

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