Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 997 · 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 55².
2. 2.Use (a + b)² = a² + 2ab + b² to find 86².
3. 3.Find the value of x² + 2xy + y² when x = 3 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 29².
5. 5.Use (a + b)² = a² + 2ab + b² to find 33².
6. 6.Find the value of x² − 2xy + y² when x = 11 and y = 8.
7. 7.Use a² − b² = (a + b)(a − b) to find 55² − 43².
8. 8.Use (a − b)² = a² − 2ab + b² to find 48².
9. 9.Use (a + b)² = a² + 2ab + b² to find 57².
10. 10.Find the value of x² + 2xy + y² when x = 4 and y = 1.
11. 11.If a + b = 3 and ab = 2, what is a² + b²?
12. 12.If a − b = 1 and ab = 12, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 71².
14. 14.Use (a + b)(a − b) = a² − b² to find 68 × 52.
15. 15.If a − b = 2 and ab = 15, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 106 × 94.
17. 17.Use a² − b² = (a + b)(a − b) to find 85² − 27².
18. 18.Find the value of x² − 2xy + y² when x = 11 and y = 2.
19. 19.Use (a + b)(a − b) = a² − b² to find 25 × 15.
20. 20.Use (a + b)² = a² + 2ab + b² to find 76².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 14 and y = 2.
23. 23.Use (a − b)² = a² − 2ab + b² to find 62².
24. 24.Use a² − b² = (a + b)(a − b) to find 38² − 13².
25. 25.Find the value of x² − 2xy + y² when x = 4 and y = 2.
26. 26.Use (a + b)(a − b) = a² − b² to find 51 × 49.
27. 27.If a − b = 1 and ab = 20, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 99².
29. 29.Use (a − b)² = a² − 2ab + b² to find 45².
30. 30.Use a² − b² = (a + b)(a − b) to find 73² − 16².
31. 31.Use (a + b)(a − b) = a² − b² to find 53 × 47.
32. 32.Use (a + b)(a − b) = a² − b² to find 31 × 29.
33. 33.Use a² − b² = (a + b)(a − b) to find 58² − 2².
34. 34.If a + b = 15 and ab = 50, what is a² + b²?
35. 35.If a − b = 9 and ab = 22, what is a² + b²?
36. 36.If a − b = 2 and ab = 8, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 22 × 18.
38. 38.Find the value of x² − y² when x = 3 and y = 1.
39. 39.Use (a − b)² = a² − 2ab + b² to find 17².
40. 40.Use (a − b)² = a² − 2ab + b² to find 91².

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