Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 187 · 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 97².
2. 2.Use (a + b)(a − b) = a² − b² to find 42 × 38.
3. 3.Use (a + b)(a − b) = a² − b² to find 48 × 32.
4. 4.Use (a + b)² = a² + 2ab + b² to find 71².
5. 5.Find the value of x² − y² when x = 9 and y = 3.
6. 6.Use (a + b)(a − b) = a² − b² to find 71 × 69.
7. 7.If a − b = 2 and ab = 24, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 22² − 17².
9. 9.If a − b = 1 and ab = 2, what is a² + b²?
10. 10.If a − b = 1 and ab = 12, what is a² + b²?
11. 11.Find the value of x² − y² when x = 11 and y = 9.
12. 12.If a − b = 4 and ab = 12, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 28² − 25².
14. 14.If a − b = 2 and ab = 3, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 25².
16. 16.Use (a − b)² = a² − 2ab + b² to find 36².
17. 17.Use a² − b² = (a + b)(a − b) to find 31² − 25².
18. 18.Use (a − b)² = a² − 2ab + b² to find 46².
19. 19.Find the value of x² + 2xy + y² when x = 15 and y = 1.
20. 20.Use (a + b)(a − b) = a² − b² to find 64 × 56.
21. 21.If a − b = 10 and ab = 24, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 63².
23. 23.Use a² − b² = (a + b)(a − b) to find 47² − 12².
24. 24.If a − b = 6 and ab = 16, what is a² + b²?
25. 25.If a − b = 9 and ab = 10, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 96².
27. 27.Use (a − b)² = a² − 2ab + b² to find 24².
28. 28.Use (a + b)(a − b) = a² − b² to find 35 × 25.
29. 29.Use (a − b)² = a² − 2ab + b² to find 19².
30. 30.Use (a + b)² = a² + 2ab + b² to find 91².
31. 31.Use (a − b)² = a² − 2ab + b² to find 66².
32. 32.Use (a − b)² = a² − 2ab + b² to find 52².
33. 33.Use a² − b² = (a + b)(a − b) to find 40² − 36².
34. 34.Use (a + b)² = a² + 2ab + b² to find 64².
35. 35.Find the value of x² − y² when x = 12 and y = 8.
36. 36.Use a² − b² = (a + b)(a − b) to find 60² − 4².
37. 37.Use a² − b² = (a + b)(a − b) to find 76² − 46².
38. 38.Use (a + b)² = a² + 2ab + b² to find 86².
39. 39.Use (a + b)² = a² + 2ab + b² to find 45².
40. 40.Use (a + b)² = a² + 2ab + b² to find 63².

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