Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 83 · 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 32².
2. 2.Use a² − b² = (a + b)(a − b) to find 22² − 6².
3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
4. 4.Use a² − b² = (a + b)(a − b) to find 45² − 20².
5. 5.If a − b = 3 and ab = 28, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 102².
7. 7.Use (a + b)(a − b) = a² − b² to find 64 × 56.
8. 8.Find the value of x² − y² when x = 15 and y = 5.
9. 9.Use a² − b² = (a + b)(a − b) to find 93² − 17².
10. 10.Use a² − b² = (a + b)(a − b) to find 49² − 30².
11. 11.Find the value of x² + 2xy + y² when x = 15 and y = 5.
12. 12.Use a² − b² = (a + b)(a − b) to find 69² − 5².
13. 13.Find the value of x² + 2xy + y² when x = 8 and y = 3.
14. 14.If a + b = 17 and ab = 72, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 24².
16. 16.Use a² − b² = (a + b)(a − b) to find 79² − 24².
17. 17.Use (a + b)(a − b) = a² − b² to find 63 × 57.
18. 18.Use (a + b)(a − b) = a² − b² to find 89 × 71.
19. 19.Use (a + b)(a − b) = a² − b² to find 41 × 39.
20. 20.Use a² − b² = (a + b)(a − b) to find 97² − 60².
21. 21.Use (a + b)(a − b) = a² − b² to find 49 × 31.
22. 22.Use (a + b)² = a² + 2ab + b² to find 88².
23. 23.Use a² − b² = (a + b)(a − b) to find 95² − 62².
24. 24.Use (a − b)² = a² − 2ab + b² to find 97².
25. 25.Use (a − b)² = a² − 2ab + b² to find 25².
26. 26.Use (a − b)² = a² − 2ab + b² to find 77².
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 3.
28. 28.Find the value of x² − y² when x = 7 and y = 2.
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 96².
31. 31.Find the value of x² + 2xy + y² when x = 3 and y = 1.
32. 32.Use (a + b)² = a² + 2ab + b² to find 36².
33. 33.Use (a + b)(a − b) = a² − b² to find 69 × 51.
34. 34.Use (a + b)(a − b) = a² − b² to find 76 × 64.
35. 35.Use a² − b² = (a + b)(a − b) to find 56² − 3².
36. 36.Use (a − b)² = a² − 2ab + b² to find 86².
37. 37.Use a² − b² = (a + b)(a − b) to find 39² − 34².
38. 38.Use a² − b² = (a + b)(a − b) to find 33² − 27².
39. 39.Use (a + b)(a − b) = a² − b² to find 59 × 41.
40. 40.Use (a − b)² = a² − 2ab + b² to find 51².

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