Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 446 · 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)(a − b) = a² − b² to find 55 × 45.
2. 2.Use (a + b)² = a² + 2ab + b² to find 27².
3. 3.If a − b = 6 and ab = 7, what is a² + b²?
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 82 × 78.
6. 6.If a + b = 8 and ab = 12, what is a² + b²?
7. 7.If a − b = 9 and ab = 10, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 58² − 16².
9. 9.Find the value of x² + 2xy + y² when x = 11 and y = 10.
10. 10.Find the value of x² + 2xy + y² when x = 12 and y = 2.
11. 11.Use a² − b² = (a + b)(a − b) to find 57² − 19².
12. 12.Use a² − b² = (a + b)(a − b) to find 29² − 11².
13. 13.Use (a + b)² = a² + 2ab + b² to find 75².
14. 14.If a + b = 8 and ab = 15, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 83².
16. 16.Find the value of x² − 2xy + y² when x = 3 and y = 1.
17. 17.Find the value of x² − 2xy + y² when x = 3 and y = 2.
18. 18.Use (a + b)² = a² + 2ab + b² to find 37².
19. 19.Use (a − b)² = a² − 2ab + b² to find 58².
20. 20.Use (a − b)² = a² − 2ab + b² to find 73².
21. 21.Use a² − b² = (a + b)(a − b) to find 53² − 38².
22. 22.Find the value of x² − y² when x = 4 and y = 2.
23. 23.Use a² − b² = (a + b)(a − b) to find 31² − 1².
24. 24.Use (a + b)² = a² + 2ab + b² to find 56².
25. 25.Use (a − b)² = a² − 2ab + b² to find 99².
26. 26.Use (a + b)² = a² + 2ab + b² to find 62².
27. 27.Find the value of x² − 2xy + y² when x = 7 and y = 5.
28. 28.Use (a + b)(a − b) = a² − b² to find 49 × 31.
29. 29.Find the value of x² − 2xy + y² when x = 12 and y = 2.
30. 30.Find the value of x² − 2xy + y² when x = 4 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 47².
32. 32.Use (a + b)² = a² + 2ab + b² to find 32².
33. 33.Use (a + b)² = a² + 2ab + b² to find 77².
34. 34.Use (a − b)² = a² − 2ab + b² to find 23².
35. 35.Use (a + b)(a − b) = a² − b² to find 46 × 34.
36. 36.Use (a + b)(a − b) = a² − b² to find 79 × 61.
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 3.
38. 38.Use (a + b)² = a² + 2ab + b² to find 92².
39. 39.Use (a + b)² = a² + 2ab + b² to find 46².
40. 40.Find the value of x² − y² when x = 15 and y = 4.

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