Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 275 · 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.Use (a − b)² = a² − 2ab + b² to find 42².
2. 2.If a − b = 2 and ab = 80, what is a² + b²?
3. 3.If a − b = 3 and ab = 4, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 53².
5. 5.Use a² − b² = (a + b)(a − b) to find 31² − 21².
6. 6.If a − b = 4 and ab = 5, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 15 and y = 7.
8. 8.Use (a + b)² = a² + 2ab + b² to find 71².
9. 9.Find the value of x² − 2xy + y² when x = 3 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 49².
11. 11.Use (a − b)² = a² − 2ab + b² to find 12².
12. 12.If a + b = 17 and ab = 66, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 93² − 5².
14. 14.Use (a + b)² = a² + 2ab + b² to find 35².
15. 15.Use a² − b² = (a + b)(a − b) to find 42² − 3².
16. 16.Use (a + b)² = a² + 2ab + b² to find 29².
17. 17.Use (a − b)² = a² − 2ab + b² to find 83².
18. 18.Use (a − b)² = a² − 2ab + b² to find 97².
19. 19.If a + b = 16 and ab = 63, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 64².
21. 21.Use (a − b)² = a² − 2ab + b² to find 66².
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 8.
23. 23.Use (a + b)(a − b) = a² − b² to find 77 × 63.
24. 24.Use (a + b)(a − b) = a² − b² to find 81 × 79.
25. 25.Use (a − b)² = a² − 2ab + b² to find 64².
26. 26.Find the value of x² − 2xy + y² when x = 6 and y = 3.
27. 27.Use a² − b² = (a + b)(a − b) to find 99² − 7².
28. 28.Use a² − b² = (a + b)(a − b) to find 75² − 10².
29. 29.Use (a + b)(a − b) = a² − b² to find 104 × 96.
30. 30.Use (a + b)(a − b) = a² − b² to find 91 × 89.
31. 31.Use (a − b)² = a² − 2ab + b² to find 39².
32. 32.Use (a + b)(a − b) = a² − b² to find 106 × 94.
33. 33.Find the value of x² + 2xy + y² when x = 14 and y = 1.
34. 34.Use (a + b)(a − b) = a² − b² to find 64 × 56.
35. 35.Use (a + b)² = a² + 2ab + b² to find 93².
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.Use (a + b)(a − b) = a² − b² to find 79 × 61.
38. 38.If a + b = 15 and ab = 50, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 51².
40. 40.Use (a + b)(a − b) = a² − b² to find 32 × 28.

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