Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 938 · 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 = 8 and y = 6.
2. 2.Use (a + b)² = a² + 2ab + b² to find 43².
3. 3.Use (a + b)² = a² + 2ab + b² to find 86².
4. 4.Use (a − b)² = a² − 2ab + b² to find 91².
5. 5.Use (a − b)² = a² − 2ab + b² to find 27².
6. 6.Use (a − b)² = a² − 2ab + b² to find 77².
7. 7.Use a² − b² = (a + b)(a − b) to find 60² − 33².
8. 8.Use (a + b)(a − b) = a² − b² to find 89 × 71.
9. 9.Find the value of x² − y² when x = 10 and y = 6.
10. 10.Use (a + b)² = a² + 2ab + b² to find 35².
11. 11.Use (a + b)² = a² + 2ab + b² to find 14².
12. 12.Use (a − b)² = a² − 2ab + b² to find 19².
13. 13.Use (a − b)² = a² − 2ab + b² to find 14².
14. 14.Find the value of x² − y² when x = 10 and y = 7.
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.If a + b = 22 and ab = 120, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 73².
18. 18.Use a² − b² = (a + b)(a − b) to find 42² − 39².
19. 19.Use (a + b)(a − b) = a² − b² to find 73 × 67.
20. 20.Use (a − b)² = a² − 2ab + b² to find 43².
21. 21.Find the value of x² − 2xy + y² when x = 13 and y = 6.
22. 22.If a − b = 2 and ab = 3, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 89² − 50².
24. 24.Use (a + b)² = a² + 2ab + b² to find 33².
25. 25.Find the value of x² + 2xy + y² when x = 6 and y = 3.
26. 26.Use (a + b)² = a² + 2ab + b² to find 96².
27. 27.Use a² − b² = (a + b)(a − b) to find 85² − 67².
28. 28.Use (a − b)² = a² − 2ab + b² to find 45².
29. 29.Use (a − b)² = a² − 2ab + b² to find 12².
30. 30.Find the value of x² − 2xy + y² when x = 4 and y = 3.
31. 31.Use (a + b)(a − b) = a² − b² to find 46 × 34.
32. 32.Use (a + b)(a − b) = a² − b² to find 81 × 79.
33. 33.Use (a − b)² = a² − 2ab + b² to find 11².
34. 34.Use (a + b)² = a² + 2ab + b² to find 26².
35. 35.Use (a + b)² = a² + 2ab + b² to find 59².
36. 36.Find the value of x² − y² when x = 11 and y = 9.
37. 37.Use (a + b)(a − b) = a² − b² to find 54 × 46.
38. 38.If a − b = 3 and ab = 40, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 7 and y = 4.
40. 40.Use (a + b)(a − b) = a² − b² to find 98 × 82.

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