Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 399 · 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 34².
2. 2.Use (a + b)(a − b) = a² − b² to find 109 × 91.
3. 3.If a − b = 1 and ab = 12, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 96².
5. 5.If a + b = 8 and ab = 7, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 94².
7. 7.Use (a + b)² = a² + 2ab + b² to find 29².
8. 8.Use a² − b² = (a + b)(a − b) to find 84² − 61².
9. 9.Use (a + b)² = a² + 2ab + b² to find 93².
10. 10.If a − b = 3 and ab = 28, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 80² − 28².
12. 12.Use (a + b)² = a² + 2ab + b² to find 17².
13. 13.Use a² − b² = (a + b)(a − b) to find 31² − 12².
14. 14.Use (a − b)² = a² − 2ab + b² to find 43².
15. 15.Use (a + b)² = a² + 2ab + b² to find 87².
16. 16.Use (a + b)² = a² + 2ab + b² to find 109².
17. 17.Use (a + b)² = a² + 2ab + b² to find 56².
18. 18.If a − b = 3 and ab = 70, what is a² + b²?
19. 19.Find the value of x² − y² when x = 5 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 95².
21. 21.Find the value of x² − 2xy + y² when x = 6 and y = 4.
22. 22.Use (a + b)² = a² + 2ab + b² to find 19².
23. 23.Find the value of x² − y² when x = 10 and y = 6.
24. 24.Use (a − b)² = a² − 2ab + b² to find 19².
25. 25.Use (a + b)² = a² + 2ab + b² to find 22².
26. 26.If a − b = 5 and ab = 50, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 83².
28. 28.If a − b = 5 and ab = 36, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 41².
30. 30.Find the value of x² − y² when x = 10 and y = 3.
31. 31.Find the value of x² − y² when x = 5 and y = 4.
32. 32.Use a² − b² = (a + b)(a − b) to find 29² − 4².
33. 33.Use a² − b² = (a + b)(a − b) to find 75² − 39².
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 3.
35. 35.Use (a + b)(a − b) = a² − b² to find 37 × 23.
36. 36.Use (a − b)² = a² − 2ab + b² to find 52².
37. 37.If a − b = 6 and ab = 55, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 97².
39. 39.Use (a + b)² = a² + 2ab + b² to find 73².
40. 40.Find the value of x² − 2xy + y² when x = 11 and y = 10.

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