Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 105 · 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.Find the value of x² − y² when x = 8 and y = 6.
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 81² − 71².
4. 4.Use (a + b)(a − b) = a² − b² to find 67 × 53.
5. 5.Use a² − b² = (a + b)(a − b) to find 76² − 28².
6. 6.Use (a − b)² = a² − 2ab + b² to find 41².
7. 7.Use (a − b)² = a² − 2ab + b² to find 69².
8. 8.Use a² − b² = (a + b)(a − b) to find 37² − 1².
9. 9.Find the value of x² − y² when x = 4 and y = 3.
10. 10.Use (a − b)² = a² − 2ab + b² to find 55².
11. 11.Find the value of x² − y² when x = 14 and y = 3.
12. 12.Use (a − b)² = a² − 2ab + b² to find 97².
13. 13.Use (a + b)² = a² + 2ab + b² to find 42².
14. 14.Find the value of x² − y² when x = 12 and y = 1.
15. 15.Find the value of x² − 2xy + y² when x = 4 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 62² − 61².
17. 17.Use (a + b)² = a² + 2ab + b² to find 89².
18. 18.Find the value of x² − 2xy + y² when x = 4 and y = 3.
19. 19.Use (a − b)² = a² − 2ab + b² to find 16².
20. 20.Use (a − b)² = a² − 2ab + b² to find 19².
21. 21.Use (a + b)(a − b) = a² − b² to find 51 × 49.
22. 22.Use (a + b)(a − b) = a² − b² to find 35 × 25.
23. 23.Use (a − b)² = a² − 2ab + b² to find 26².
24. 24.Use (a + b)(a − b) = a² − b² to find 104 × 96.
25. 25.Use a² − b² = (a + b)(a − b) to find 73² − 51².
26. 26.If a − b = 8 and ab = 33, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 64².
28. 28.Use (a + b)² = a² + 2ab + b² to find 36².
29. 29.Use a² − b² = (a + b)(a − b) to find 82² − 50².
30. 30.Use (a + b)² = a² + 2ab + b² to find 37².
31. 31.Use (a + b)(a − b) = a² − b² to find 103 × 97.
32. 32.Find the value of x² − y² when x = 10 and y = 3.
33. 33.Use (a + b)² = a² + 2ab + b² to find 86².
34. 34.Find the value of x² + 2xy + y² when x = 12 and y = 5.
35. 35.Use a² − b² = (a + b)(a − b) to find 74² − 71².
36. 36.Use a² − b² = (a + b)(a − b) to find 20² − 15².
37. 37.Use (a − b)² = a² − 2ab + b² to find 45².
38. 38.Use (a + b)² = a² + 2ab + b² to find 97².
39. 39.If a − b = 6 and ab = 16, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 42 × 38.

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