Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 97 · 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 = 2 and ab = 35, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 34² − 13².
3. 3.Use (a − b)² = a² − 2ab + b² to find 88².
4. 4.Find the value of x² − y² when x = 15 and y = 7.
5. 5.Use (a + b)² = a² + 2ab + b² to find 16².
6. 6.Use a² − b² = (a + b)(a − b) to find 67² − 33².
7. 7.Use (a + b)² = a² + 2ab + b² to find 92².
8. 8.Use (a + b)² = a² + 2ab + b² to find 101².
9. 9.Use (a − b)² = a² − 2ab + b² to find 45².
10. 10.If a − b = 1 and ab = 6, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 104 × 96.
12. 12.If a − b = 10 and ab = 24, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 53².
14. 14.Use (a + b)² = a² + 2ab + b² to find 105².
15. 15.Use (a − b)² = a² − 2ab + b² to find 12².
16. 16.Use a² − b² = (a + b)(a − b) to find 22² − 9².
17. 17.Find the value of x² − y² when x = 4 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 47².
19. 19.Use (a + b)² = a² + 2ab + b² to find 28².
20. 20.If a − b = 5 and ab = 36, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 49² − 18².
22. 22.Find the value of x² + 2xy + y² when x = 5 and y = 3.
23. 23.If a + b = 9 and ab = 20, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 53 × 47.
25. 25.Use a² − b² = (a + b)(a − b) to find 96² − 40².
26. 26.Use (a + b)² = a² + 2ab + b² to find 87².
27. 27.Use (a + b)² = a² + 2ab + b² to find 86².
28. 28.Use (a + b)² = a² + 2ab + b² to find 99².
29. 29.Find the value of x² − y² when x = 3 and y = 2.
30. 30.Use (a − b)² = a² − 2ab + b² to find 16².
31. 31.Use (a + b)² = a² + 2ab + b² to find 75².
32. 32.Use a² − b² = (a + b)(a − b) to find 96² − 79².
33. 33.If a − b = 2 and ab = 3, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 50² − 36².
35. 35.Use (a + b)² = a² + 2ab + b² to find 43².
36. 36.Use (a + b)² = a² + 2ab + b² to find 69².
37. 37.Use (a − b)² = a² − 2ab + b² to find 64².
38. 38.If a − b = 8 and ab = 9, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 5 and y = 4.
40. 40.Use (a + b)(a − b) = a² − b² to find 91 × 89.

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