Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 960 · 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 66².
2. 2.Use (a − b)² = a² − 2ab + b² to find 59².
3. 3.Use (a − b)² = a² − 2ab + b² to find 83².
4. 4.Use a² − b² = (a + b)(a − b) to find 80² − 53².
5. 5.If a − b = 1 and ab = 72, what is a² + b²?
6. 6.If a + b = 16 and ab = 48, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 99².
8. 8.Use (a + b)² = a² + 2ab + b² to find 69².
9. 9.Use a² − b² = (a + b)(a − b) to find 59² − 3².
10. 10.If a + b = 12 and ab = 11, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 21² − 6².
12. 12.Use (a + b)² = a² + 2ab + b² to find 87².
13. 13.Use (a + b)² = a² + 2ab + b² to find 42².
14. 14.Use (a + b)² = a² + 2ab + b² to find 71².
15. 15.Use (a + b)² = a² + 2ab + b² to find 66².
16. 16.If a − b = 5 and ab = 66, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 43² − 12².
18. 18.Use (a − b)² = a² − 2ab + b² to find 73².
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 33² − 4².
21. 21.Use a² − b² = (a + b)(a − b) to find 27² − 11².
22. 22.Use (a + b)(a − b) = a² − b² to find 41 × 39.
23. 23.If a + b = 9 and ab = 8, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 16².
25. 25.Use a² − b² = (a + b)(a − b) to find 60² − 48².
26. 26.Use (a − b)² = a² − 2ab + b² to find 61².
27. 27.Use (a − b)² = a² − 2ab + b² to find 75².
28. 28.Use (a + b)² = a² + 2ab + b² to find 51².
29. 29.If a + b = 22 and ab = 120, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 53².
31. 31.Use (a + b)² = a² + 2ab + b² to find 82².
32. 32.Use (a − b)² = a² − 2ab + b² to find 91².
33. 33.Use a² − b² = (a + b)(a − b) to find 59² − 38².
34. 34.Find the value of x² − y² when x = 8 and y = 2.
35. 35.Use (a + b)² = a² + 2ab + b² to find 37².
36. 36.Use (a − b)² = a² − 2ab + b² to find 26².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 28² − 19².
39. 39.If a − b = 2 and ab = 63, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 66 × 54.

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