Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 814 · 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 = 3 and ab = 2, what is a² + b²?
2. 2.If a + b = 8 and ab = 7, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 99².
4. 4.If a + b = 9 and ab = 20, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 16².
6. 6.If a − b = 7 and ab = 18, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 91².
8. 8.Use (a − b)² = a² − 2ab + b² to find 27².
9. 9.Use (a − b)² = a² − 2ab + b² to find 25².
10. 10.If a − b = 1 and ab = 2, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 22².
12. 12.Use (a − b)² = a² − 2ab + b² to find 55².
13. 13.Use a² − b² = (a + b)(a − b) to find 62² − 10².
14. 14.Use a² − b² = (a + b)(a − b) to find 75² − 26².
15. 15.Use (a + b)(a − b) = a² − b² to find 27 × 13.
16. 16.Use a² − b² = (a + b)(a − b) to find 65² − 49².
17. 17.Find the value of x² + 2xy + y² when x = 8 and y = 7.
18. 18.Use a² − b² = (a + b)(a − b) to find 67² − 58².
19. 19.If a + b = 13 and ab = 22, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 46² − 28².
21. 21.Use (a + b)² = a² + 2ab + b² to find 43².
22. 22.Find the value of x² − y² when x = 14 and y = 8.
23. 23.If a − b = 1 and ab = 30, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 53².
25. 25.Use (a + b)² = a² + 2ab + b² to find 24².
26. 26.Use (a − b)² = a² − 2ab + b² to find 69².
27. 27.Use (a + b)² = a² + 2ab + b² to find 64².
28. 28.Use (a + b)(a − b) = a² − b² to find 99 × 81.
29. 29.Use a² − b² = (a + b)(a − b) to find 29² − 24².
30. 30.Use (a + b)² = a² + 2ab + b² to find 77².
31. 31.Use (a + b)² = a² + 2ab + b² to find 36².
32. 32.Use (a − b)² = a² − 2ab + b² to find 68².
33. 33.If a + b = 15 and ab = 54, what is a² + b²?
34. 34.Find the value of x² − y² when x = 7 and y = 4.
35. 35.Find the value of x² + 2xy + y² when x = 6 and y = 4.
36. 36.Use (a + b)² = a² + 2ab + b² to find 87².
37. 37.Use (a + b)(a − b) = a² − b² to find 46 × 34.
38. 38.Use a² − b² = (a + b)(a − b) to find 60² − 26².
39. 39.Find the value of x² + 2xy + y² when x = 6 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 30² − 15².

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