Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 63 · 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 63² − 35².
2. 2.Use (a + b)² = a² + 2ab + b² to find 27².
3. 3.Use a² − b² = (a + b)(a − b) to find 47² − 35².
4. 4.Use (a + b)(a − b) = a² − b² to find 52 × 48.
5. 5.Use a² − b² = (a + b)(a − b) to find 75² − 17².
6. 6.Find the value of x² − y² when x = 12 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 25 × 15.
8. 8.Use a² − b² = (a + b)(a − b) to find 81² − 70².
9. 9.Find the value of x² − 2xy + y² when x = 9 and y = 8.
10. 10.Use a² − b² = (a + b)(a − b) to find 78² − 9².
11. 11.Use (a + b)(a − b) = a² − b² to find 99 × 81.
12. 12.Find the value of x² + 2xy + y² when x = 15 and y = 5.
13. 13.If a + b = 13 and ab = 12, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 106².
15. 15.Use (a + b)² = a² + 2ab + b² to find 92².
16. 16.Use (a + b)² = a² + 2ab + b² to find 16².
17. 17.Use (a + b)(a − b) = a² − b² to find 55 × 45.
18. 18.If a − b = 3 and ab = 4, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 97².
20. 20.Use (a + b)² = a² + 2ab + b² to find 28².
21. 21.Use (a − b)² = a² − 2ab + b² to find 86².
22. 22.Use (a + b)² = a² + 2ab + b² to find 23².
23. 23.Use (a + b)² = a² + 2ab + b² to find 85².
24. 24.Use (a − b)² = a² − 2ab + b² to find 77².
25. 25.Use (a + b)² = a² + 2ab + b² to find 52².
26. 26.Use (a − b)² = a² − 2ab + b² to find 18².
27. 27.Use a² − b² = (a + b)(a − b) to find 25² − 12².
28. 28.Use a² − b² = (a + b)(a − b) to find 86² − 56².
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.If a + b = 4 and ab = 3, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 57² − 31².
32. 32.Use (a + b)² = a² + 2ab + b² to find 76².
33. 33.Use (a + b)² = a² + 2ab + b² to find 13².
34. 34.Use (a + b)² = a² + 2ab + b² to find 49².
35. 35.If a + b = 12 and ab = 11, what is a² + b²?
36. 36.If a − b = 5 and ab = 14, what is a² + b²?
37. 37.If a + b = 6 and ab = 8, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 71 × 69.
39. 39.If a − b = 6 and ab = 7, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 66².

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