Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 936 · 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 27².
2. 2.Use a² − b² = (a + b)(a − b) to find 97² − 88².
3. 3.If a − b = 3 and ab = 10, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 72².
5. 5.Use a² − b² = (a + b)(a − b) to find 97² − 9².
6. 6.Use a² − b² = (a + b)(a − b) to find 57² − 14².
7. 7.Use a² − b² = (a + b)(a − b) to find 34² − 20².
8. 8.Find the value of x² − y² when x = 14 and y = 2.
9. 9.Use (a − b)² = a² − 2ab + b² to find 84².
10. 10.Find the value of x² − 2xy + y² when x = 5 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 12².
12. 12.Use (a + b)² = a² + 2ab + b² to find 58².
13. 13.Use (a − b)² = a² − 2ab + b² to find 53².
14. 14.If a − b = 7 and ab = 18, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 33² − 15².
17. 17.Find the value of x² − 2xy + y² when x = 9 and y = 2.
18. 18.Use a² − b² = (a + b)(a − b) to find 48² − 17².
19. 19.Use (a − b)² = a² − 2ab + b² to find 54².
20. 20.Use (a − b)² = a² − 2ab + b² to find 18².
21. 21.Find the value of x² − 2xy + y² when x = 15 and y = 1.
22. 22.If a + b = 20 and ab = 96, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 71 × 69.
24. 24.If a − b = 1 and ab = 2, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 73² − 9².
26. 26.Use (a + b)² = a² + 2ab + b² to find 16².
27. 27.Use (a + b)² = a² + 2ab + b² to find 106².
28. 28.If a − b = 6 and ab = 16, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 16².
30. 30.Use a² − b² = (a + b)(a − b) to find 89² − 21².
31. 31.Use (a − b)² = a² − 2ab + b² to find 56².
32. 32.Find the value of x² − y² when x = 12 and y = 11.
33. 33.Use (a − b)² = a² − 2ab + b² to find 88².
34. 34.Use (a − b)² = a² − 2ab + b² to find 58².
35. 35.If a − b = 9 and ab = 36, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 38².
37. 37.Use (a + b)² = a² + 2ab + b² to find 56².
38. 38.Use a² − b² = (a + b)(a − b) to find 25² − 24².
39. 39.Use a² − b² = (a + b)(a − b) to find 90² − 52².
40. 40.Use a² − b² = (a + b)(a − b) to find 61² − 53².

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