Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 93 · 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 25².
2. 2.Use a² − b² = (a + b)(a − b) to find 32² − 21².
3. 3.Use (a − b)² = a² − 2ab + b² to find 11².
4. 4.Find the value of x² − 2xy + y² when x = 12 and y = 9.
5. 5.If a − b = 1 and ab = 12, what is a² + b²?
6. 6.If a + b = 12 and ab = 35, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 18².
8. 8.Use (a + b)² = a² + 2ab + b² to find 74².
9. 9.Use (a + b)² = a² + 2ab + b² to find 53².
10. 10.If a + b = 11 and ab = 18, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 21².
12. 12.If a − b = 1 and ab = 2, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 12 and y = 5.
14. 14.Use (a + b)² = a² + 2ab + b² to find 56².
15. 15.Use (a + b)² = a² + 2ab + b² to find 39².
16. 16.Use (a − b)² = a² − 2ab + b² to find 19².
17. 17.Find the value of x² − y² when x = 12 and y = 7.
18. 18.If a − b = 2 and ab = 3, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 7.
20. 20.Use (a − b)² = a² − 2ab + b² to find 38².
21. 21.If a − b = 1 and ab = 20, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 98².
23. 23.Use (a + b)(a − b) = a² − b² to find 53 × 47.
24. 24.If a + b = 5 and ab = 4, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 74².
26. 26.Use a² − b² = (a + b)(a − b) to find 42² − 11².
27. 27.Use (a + b)² = a² + 2ab + b² to find 16².
28. 28.If a + b = 15 and ab = 44, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 38² − 31².
30. 30.Use a² − b² = (a + b)(a − b) to find 37² − 28².
31. 31.If a + b = 6 and ab = 5, what is a² + b²?
32. 32.Find the value of x² − y² when x = 4 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 15².
34. 34.Use (a + b)(a − b) = a² − b² to find 63 × 57.
35. 35.If a − b = 5 and ab = 36, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 11 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 33² − 12².
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.Use (a − b)² = a² − 2ab + b² to find 71².
40. 40.Use (a − b)² = a² − 2ab + b² to find 73².

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