Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 615 · 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 + 2xy + y² when x = 8 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 23² − 1².
3. 3.Use (a + b)² = a² + 2ab + b² to find 53².
4. 4.Use (a − b)² = a² − 2ab + b² to find 73².
5. 5.Use a² − b² = (a + b)(a − b) to find 47² − 43².
6. 6.If a − b = 4 and ab = 45, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 97².
8. 8.Use (a + b)² = a² + 2ab + b² to find 76².
9. 9.Use a² − b² = (a + b)(a − b) to find 60² − 3².
10. 10.Find the value of x² − y² when x = 5 and y = 4.
11. 11.Use (a − b)² = a² − 2ab + b² to find 61².
12. 12.Use a² − b² = (a + b)(a − b) to find 98² − 22².
13. 13.Use (a + b)² = a² + 2ab + b² to find 42².
14. 14.If a − b = 4 and ab = 21, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 53 × 47.
16. 16.If a + b = 7 and ab = 12, what is a² + b²?
17. 17.Find the value of x² − y² when x = 6 and y = 5.
18. 18.Use (a + b)² = a² + 2ab + b² to find 96².
19. 19.Use (a − b)² = a² − 2ab + b² to find 35².
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 2.
22. 22.Find the value of x² − 2xy + y² when x = 10 and y = 3.
23. 23.Use (a + b)² = a² + 2ab + b² to find 21².
24. 24.If a − b = 5 and ab = 24, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 3 and y = 2.
26. 26.Use a² − b² = (a + b)(a − b) to find 78² − 69².
27. 27.Find the value of x² + 2xy + y² when x = 5 and y = 4.
28. 28.Use (a − b)² = a² − 2ab + b² to find 21².
29. 29.Find the value of x² − 2xy + y² when x = 8 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 45² − 19².
31. 31.Use a² − b² = (a + b)(a − b) to find 57² − 30².
32. 32.Use (a − b)² = a² − 2ab + b² to find 99².
33. 33.Use (a + b)² = a² + 2ab + b² to find 13².
34. 34.Use (a − b)² = a² − 2ab + b² to find 77².
35. 35.Use a² − b² = (a + b)(a − b) to find 49² − 22².
36. 36.Use (a + b)(a − b) = a² − b² to find 73 × 67.
37. 37.Use (a + b)² = a² + 2ab + b² to find 38².
38. 38.If a + b = 8 and ab = 12, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 95 × 85.
40. 40.Use (a − b)² = a² − 2ab + b² to find 92².

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