Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 902 · 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 86².
2. 2.Use a² − b² = (a + b)(a − b) to find 84² − 59².
3. 3.If a − b = 3 and ab = 10, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 31².
5. 5.If a − b = 4 and ab = 21, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 97².
7. 7.Use (a + b)² = a² + 2ab + b² to find 34².
8. 8.If a − b = 1 and ab = 42, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 94² − 80².
10. 10.If a − b = 6 and ab = 16, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 29².
12. 12.Use (a + b)(a − b) = a² − b² to find 57 × 43.
13. 13.Find the value of x² − 2xy + y² when x = 10 and y = 5.
14. 14.Find the value of x² − 2xy + y² when x = 6 and y = 3.
15. 15.If a − b = 6 and ab = 40, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 45².
17. 17.Use (a − b)² = a² − 2ab + b² to find 81².
18. 18.Use (a + b)(a − b) = a² − b² to find 39 × 21.
19. 19.Find the value of x² − y² when x = 4 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 74² − 53².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.If a − b = 7 and ab = 8, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 11 and y = 8.
24. 24.Use a² − b² = (a + b)(a − b) to find 27² − 14².
25. 25.Use (a − b)² = a² − 2ab + b² to find 69².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.If a − b = 5 and ab = 50, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 53².
29. 29.Use (a + b)(a − b) = a² − b² to find 29 × 11.
30. 30.Use (a + b)² = a² + 2ab + b² to find 45².
31. 31.If a − b = 1 and ab = 12, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 41 × 39.
33. 33.Find the value of x² − 2xy + y² when x = 9 and y = 4.
34. 34.Use (a + b)² = a² + 2ab + b² to find 76².
35. 35.Use (a + b)² = a² + 2ab + b² to find 12².
36. 36.Use (a + b)² = a² + 2ab + b² to find 71².
37. 37.Find the value of x² + 2xy + y² when x = 14 and y = 12.
38. 38.Use a² − b² = (a + b)(a − b) to find 24² − 3².
39. 39.Use (a + b)² = a² + 2ab + b² to find 106².
40. 40.Use a² − b² = (a + b)(a − b) to find 62² − 17².

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