Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 666 · 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.If a − b = 10 and ab = 11, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 4 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 78².
4. 4.Find the value of x² − y² when x = 9 and y = 6.
5. 5.If a − b = 1 and ab = 42, what is a² + b²?
6. 6.Find the value of x² − 2xy + y² when x = 14 and y = 10.
7. 7.Use (a + b)² = a² + 2ab + b² to find 85².
8. 8.Find the value of x² − y² when x = 12 and y = 2.
9. 9.Find the value of x² + 2xy + y² when x = 7 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 96².
11. 11.Find the value of x² − y² when x = 8 and y = 1.
12. 12.Use (a − b)² = a² − 2ab + b² to find 79².
13. 13.If a − b = 9 and ab = 10, what is a² + b²?
14. 14.If a − b = 3 and ab = 10, what is a² + b²?
15. 15.If a + b = 17 and ab = 60, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 76².
17. 17.Use a² − b² = (a + b)(a − b) to find 63² − 60².
18. 18.Find the value of x² + 2xy + y² when x = 11 and y = 8.
19. 19.Use a² − b² = (a + b)(a − b) to find 52² − 37².
20. 20.Find the value of x² + 2xy + y² when x = 4 and y = 2.
21. 21.Use a² − b² = (a + b)(a − b) to find 84² − 45².
22. 22.Use (a − b)² = a² − 2ab + b² to find 39².
23. 23.Use (a + b)(a − b) = a² − b² to find 69 × 51.
24. 24.Use (a − b)² = a² − 2ab + b² to find 21².
25. 25.Use (a − b)² = a² − 2ab + b² to find 34².
26. 26.Find the value of x² + 2xy + y² when x = 8 and y = 4.
27. 27.If a + b = 19 and ab = 84, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 102².
30. 30.Use (a − b)² = a² − 2ab + b² to find 45².
31. 31.Use (a + b)² = a² + 2ab + b² to find 16².
32. 32.If a − b = 3 and ab = 70, what is a² + b²?
33. 33.If a − b = 6 and ab = 7, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 11 and y = 4.
35. 35.Use (a − b)² = a² − 2ab + b² to find 85².
36. 36.Find the value of x² − y² when x = 4 and y = 2.
37. 37.Use (a − b)² = a² − 2ab + b² to find 83².
38. 38.Use (a + b)² = a² + 2ab + b² to find 53².
39. 39.Use a² − b² = (a + b)(a − b) to find 73² − 56².
40. 40.Find the value of x² − y² when x = 13 and y = 5.

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