Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 907 · 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 − 2xy + y² when x = 9 and y = 2.
2. 2.Use (a + b)² = a² + 2ab + b² to find 31².
3. 3.Use (a + b)² = a² + 2ab + b² to find 69².
4. 4.Use (a − b)² = a² − 2ab + b² to find 97².
5. 5.Use a² − b² = (a + b)(a − b) to find 52² − 31².
6. 6.If a − b = 2 and ab = 3, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 105 × 95.
8. 8.Use (a + b)² = a² + 2ab + b² to find 61².
9. 9.Use (a + b)² = a² + 2ab + b² to find 12².
10. 10.Use (a + b)² = a² + 2ab + b² to find 37².
11. 11.Use (a − b)² = a² − 2ab + b² to find 14².
12. 12.If a − b = 5 and ab = 36, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 95² − 9².
14. 14.Use (a + b)² = a² + 2ab + b² to find 91².
15. 15.Use a² − b² = (a + b)(a − b) to find 48² − 39².
16. 16.If a + b = 4 and ab = 3, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 62² − 12².
18. 18.Use (a − b)² = a² − 2ab + b² to find 11².
19. 19.If a + b = 12 and ab = 27, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 102².
21. 21.Find the value of x² − 2xy + y² when x = 7 and y = 1.
22. 22.Use a² − b² = (a + b)(a − b) to find 34² − 27².
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 5.
24. 24.If a − b = 7 and ab = 18, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 3 and y = 1.
26. 26.Use (a − b)² = a² − 2ab + b² to find 76².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 4.
28. 28.Use (a + b)² = a² + 2ab + b² to find 24².
29. 29.Use (a + b)(a − b) = a² − b² to find 27 × 13.
30. 30.Use (a + b)(a − b) = a² − b² to find 26 × 14.
31. 31.Find the value of x² − y² when x = 7 and y = 2.
32. 32.Use (a − b)² = a² − 2ab + b² to find 31².
33. 33.Use (a + b)² = a² + 2ab + b² to find 104².
34. 34.If a − b = 1 and ab = 20, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 68² − 16².
36. 36.Find the value of x² − 2xy + y² when x = 11 and y = 6.
37. 37.Use (a − b)² = a² − 2ab + b² to find 22².
38. 38.Use a² − b² = (a + b)(a − b) to find 97² − 2².
39. 39.Use (a − b)² = a² − 2ab + b² to find 46².
40. 40.Use (a + b)(a − b) = a² − b² to find 39 × 21.

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