Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 437 · 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 a² − b² = (a + b)(a − b) to find 22² − 2².
2. 2.Use a² − b² = (a + b)(a − b) to find 50² − 12².
3. 3.Use (a + b)(a − b) = a² − b² to find 96 × 84.
4. 4.Use (a − b)² = a² − 2ab + b² to find 82².
5. 5.If a − b = 5 and ab = 36, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 54² − 4².
7. 7.Use (a + b)(a − b) = a² − b² to find 81 × 79.
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 2.
9. 9.Use (a − b)² = a² − 2ab + b² to find 83².
10. 10.Use (a + b)(a − b) = a² − b² to find 31 × 29.
11. 11.Use (a + b)² = a² + 2ab + b² to find 83².
12. 12.Use (a − b)² = a² − 2ab + b² to find 25².
13. 13.Use a² − b² = (a + b)(a − b) to find 53² − 48².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 87² − 30².
16. 16.If a − b = 2 and ab = 15, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 15 and y = 3.
18. 18.Use a² − b² = (a + b)(a − b) to find 97² − 24².
19. 19.Find the value of x² + 2xy + y² when x = 6 and y = 2.
20. 20.Use (a + b)² = a² + 2ab + b² to find 51².
21. 21.Use (a − b)² = a² − 2ab + b² to find 31².
22. 22.Use (a − b)² = a² − 2ab + b² to find 41².
23. 23.If a + b = 9 and ab = 18, what is a² + b²?
24. 24.If a + b = 13 and ab = 22, what is a² + b²?
25. 25.If a − b = 4 and ab = 60, what is a² + b²?
26. 26.Find the value of x² − y² when x = 5 and y = 3.
27. 27.Use (a + b)(a − b) = a² − b² to find 89 × 71.
28. 28.Use a² − b² = (a + b)(a − b) to find 38² − 35².
29. 29.Use (a + b)² = a² + 2ab + b² to find 103².
30. 30.If a + b = 6 and ab = 8, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 51².
32. 32.Use (a + b)² = a² + 2ab + b² to find 22².
33. 33.Find the value of x² + 2xy + y² when x = 9 and y = 1.
34. 34.If a − b = 6 and ab = 7, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 57 × 43.
36. 36.Use a² − b² = (a + b)(a − b) to find 88² − 51².
37. 37.Use (a + b)² = a² + 2ab + b² to find 58².
38. 38.Use a² − b² = (a + b)(a − b) to find 36² − 24².
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 1.
40. 40.Use (a + b)(a − b) = a² − b² to find 101 × 99.

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