Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 66 · 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.Find the value of x² − y² when x = 3 and y = 1.
2. 2.Find the value of x² − 2xy + y² when x = 10 and y = 3.
3. 3.Find the value of x² − y² when x = 3 and y = 2.
4. 4.Use (a − b)² = a² − 2ab + b² to find 21².
5. 5.If a − b = 2 and ab = 8, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 81 × 79.
7. 7.Use (a + b)² = a² + 2ab + b² to find 81².
8. 8.Use (a + b)(a − b) = a² − b² to find 54 × 46.
9. 9.Use (a + b)² = a² + 2ab + b² to find 17².
10. 10.Use (a + b)² = a² + 2ab + b² to find 107².
11. 11.If a − b = 3 and ab = 54, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 29².
13. 13.If a − b = 4 and ab = 32, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 30² − 4².
15. 15.Find the value of x² − 2xy + y² when x = 9 and y = 5.
16. 16.If a + b = 10 and ab = 9, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 22².
18. 18.Use (a − b)² = a² − 2ab + b² to find 64².
19. 19.If a − b = 1 and ab = 2, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 49 × 31.
21. 21.Use (a + b)² = a² + 2ab + b² to find 98².
22. 22.Find the value of x² − 2xy + y² when x = 6 and y = 4.
23. 23.Use (a − b)² = a² − 2ab + b² to find 37².
24. 24.Use (a + b)(a − b) = a² − b² to find 64 × 56.
25. 25.If a − b = 4 and ab = 96, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 27².
27. 27.Find the value of x² − y² when x = 14 and y = 4.
28. 28.Use (a − b)² = a² − 2ab + b² to find 16².
29. 29.Use (a + b)² = a² + 2ab + b² to find 53².
30. 30.Use (a + b)² = a² + 2ab + b² to find 62².
31. 31.Use (a − b)² = a² − 2ab + b² to find 78².
32. 32.Use (a + b)² = a² + 2ab + b² to find 61².
33. 33.Use (a + b)² = a² + 2ab + b² to find 16².
34. 34.Use (a + b)² = a² + 2ab + b² to find 102².
35. 35.Find the value of x² + 2xy + y² when x = 13 and y = 7.
36. 36.Use (a − b)² = a² − 2ab + b² to find 68².
37. 37.Use a² − b² = (a + b)(a − b) to find 35² − 5².
38. 38.Use (a + b)(a − b) = a² − b² to find 42 × 38.
39. 39.Use (a + b)² = a² + 2ab + b² to find 52².
40. 40.Use (a + b)(a − b) = a² − b² to find 105 × 95.

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