Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 968 · 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.If a − b = 5 and ab = 6, what is a² + b²?
2. 2.Find the value of x² − y² when x = 4 and y = 3.
3. 3.Use a² − b² = (a + b)(a − b) to find 99² − 85².
4. 4.Use (a + b)² = a² + 2ab + b² to find 106².
5. 5.Use (a − b)² = a² − 2ab + b² to find 49².
6. 6.Use (a − b)² = a² − 2ab + b² to find 37².
7. 7.Use (a + b)² = a² + 2ab + b² to find 13².
8. 8.Use (a + b)(a − b) = a² − b² to find 58 × 42.
9. 9.Use (a − b)² = a² − 2ab + b² to find 78².
10. 10.Find the value of x² − y² when x = 13 and y = 9.
11. 11.Use (a − b)² = a² − 2ab + b² to find 54².
12. 12.Use (a − b)² = a² − 2ab + b² to find 28².
13. 13.If a + b = 17 and ab = 66, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 29² − 24².
15. 15.If a + b = 18 and ab = 72, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 52².
17. 17.Use (a − b)² = a² − 2ab + b² to find 83².
18. 18.If a + b = 15 and ab = 50, what is a² + b²?
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 22².
21. 21.Use (a + b)² = a² + 2ab + b² to find 84².
22. 22.Use (a − b)² = a² − 2ab + b² to find 76².
23. 23.Use (a − b)² = a² − 2ab + b² to find 88².
24. 24.Use a² − b² = (a + b)(a − b) to find 96² − 66².
25. 25.Use (a + b)² = a² + 2ab + b² to find 69².
26. 26.If a − b = 6 and ab = 16, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 107².
28. 28.Use (a + b)(a − b) = a² − b² to find 94 × 86.
29. 29.Use (a + b)² = a² + 2ab + b² to find 14².
30. 30.Use (a − b)² = a² − 2ab + b² to find 38².
31. 31.Use (a + b)(a − b) = a² − b² to find 45 × 35.
32. 32.Use (a + b)(a − b) = a² − b² to find 21 × 19.
33. 33.Use a² − b² = (a + b)(a − b) to find 34² − 12².
34. 34.Use (a + b)² = a² + 2ab + b² to find 98².
35. 35.Use (a − b)² = a² − 2ab + b² to find 47².
36. 36.Use (a − b)² = a² − 2ab + b² to find 13².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 1.
38. 38.If a − b = 3 and ab = 54, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 26² − 17².
40. 40.Use a² − b² = (a + b)(a − b) to find 42² − 26².

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