Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 879 · 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 81².
2. 2.Use a² − b² = (a + b)(a − b) to find 38² − 3².
3. 3.Use (a + b)(a − b) = a² − b² to find 105 × 95.
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 11.
5. 5.Use (a + b)² = a² + 2ab + b² to find 35².
6. 6.Use (a − b)² = a² − 2ab + b² to find 28².
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 1.
8. 8.Use a² − b² = (a + b)(a − b) to find 66² − 12².
9. 9.Use (a + b)² = a² + 2ab + b² to find 85².
10. 10.Use a² − b² = (a + b)(a − b) to find 20² − 19².
11. 11.Use (a + b)(a − b) = a² − b² to find 21 × 19.
12. 12.If a − b = 1 and ab = 30, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 78² − 73².
14. 14.Use a² − b² = (a + b)(a − b) to find 26² − 15².
15. 15.Use (a − b)² = a² − 2ab + b² to find 88².
16. 16.Use (a + b)² = a² + 2ab + b² to find 71².
17. 17.If a + b = 13 and ab = 42, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 65².
19. 19.Use (a + b)(a − b) = a² − b² to find 61 × 59.
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 37².
22. 22.Use a² − b² = (a + b)(a − b) to find 87² − 13².
23. 23.Use (a − b)² = a² − 2ab + b² to find 55².
24. 24.Use (a − b)² = a² − 2ab + b² to find 98².
25. 25.Find the value of x² + 2xy + y² when x = 6 and y = 3.
26. 26.Use (a + b)(a − b) = a² − b² to find 82 × 78.
27. 27.Use (a + b)(a − b) = a² − b² to find 108 × 92.
28. 28.If a − b = 1 and ab = 2, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 51².
30. 30.Use (a + b)² = a² + 2ab + b² to find 53².
31. 31.Find the value of x² − y² when x = 13 and y = 3.
32. 32.Use (a + b)² = a² + 2ab + b² to find 106².
33. 33.Use (a − b)² = a² − 2ab + b² to find 17².
34. 34.Use a² − b² = (a + b)(a − b) to find 73² − 56².
35. 35.Use (a + b)² = a² + 2ab + b² to find 17².
36. 36.If a − b = 2 and ab = 120, what is a² + b²?
37. 37.Find the value of x² − y² when x = 8 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 49² − 31².
39. 39.Use (a + b)² = a² + 2ab + b² to find 37².
40. 40.Use a² − b² = (a + b)(a − b) to find 59² − 32².

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