Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 809 · 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 36².
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 49².
4. 4.Use (a − b)² = a² − 2ab + b² to find 77².
5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
6. 6.Use (a + b)² = a² + 2ab + b² to find 99².
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 6.
8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 6.
9. 9.Use (a − b)² = a² − 2ab + b² to find 29².
10. 10.Use (a − b)² = a² − 2ab + b² to find 22².
11. 11.Use a² − b² = (a + b)(a − b) to find 59² − 25².
12. 12.Use (a + b)(a − b) = a² − b² to find 23 × 17.
13. 13.If a − b = 2 and ab = 24, what is a² + b²?
14. 14.If a + b = 20 and ab = 96, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 28².
16. 16.If a − b = 2 and ab = 120, what is a² + b²?
17. 17.If a − b = 2 and ab = 35, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 61².
19. 19.Use (a − b)² = a² − 2ab + b² to find 52².
20. 20.Use (a + b)(a − b) = a² − b² to find 71 × 69.
21. 21.Use (a + b)² = a² + 2ab + b² to find 66².
22. 22.If a + b = 11 and ab = 18, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 79² − 13².
24. 24.Use (a − b)² = a² − 2ab + b² to find 24².
25. 25.Find the value of x² + 2xy + y² when x = 6 and y = 2.
26. 26.Find the value of x² + 2xy + y² when x = 12 and y = 6.
27. 27.If a + b = 13 and ab = 30, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 53² − 19².
29. 29.Use (a − b)² = a² − 2ab + b² to find 19².
30. 30.Use a² − b² = (a + b)(a − b) to find 77² − 65².
31. 31.Use a² − b² = (a + b)(a − b) to find 42² − 27².
32. 32.Use a² − b² = (a + b)(a − b) to find 61² − 38².
33. 33.Find the value of x² + 2xy + y² when x = 8 and y = 2.
34. 34.Use (a − b)² = a² − 2ab + b² to find 85².
35. 35.Use (a − b)² = a² − 2ab + b² to find 62².
36. 36.Use a² − b² = (a + b)(a − b) to find 96² − 72².
37. 37.Use (a + b)² = a² + 2ab + b² to find 34².
38. 38.Use (a + b)² = a² + 2ab + b² to find 72².
39. 39.Find the value of x² − y² when x = 4 and y = 3.
40. 40.If a − b = 4 and ab = 12, what is a² + b²?

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