Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 778 · 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 82 × 78.
2. 2.Use a² − b² = (a + b)(a − b) to find 75² − 47².
3. 3.Use (a − b)² = a² − 2ab + b² to find 25².
4. 4.Use (a + b)² = a² + 2ab + b² to find 23².
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 68².
7. 7.If a + b = 16 and ab = 55, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 99² − 35².
9. 9.Use a² − b² = (a + b)(a − b) to find 30² − 11².
10. 10.Use (a − b)² = a² − 2ab + b² to find 66².
11. 11.Use (a + b)² = a² + 2ab + b² to find 109².
12. 12.Use (a + b)² = a² + 2ab + b² to find 106².
13. 13.Use (a − b)² = a² − 2ab + b² to find 64².
14. 14.Find the value of x² − y² when x = 15 and y = 9.
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 49².
17. 17.Use (a + b)² = a² + 2ab + b² to find 63².
18. 18.Use (a + b)² = a² + 2ab + b² to find 28².
19. 19.Use (a − b)² = a² − 2ab + b² to find 39².
20. 20.Use (a + b)² = a² + 2ab + b² to find 18².
21. 21.Use (a − b)² = a² − 2ab + b² to find 41².
22. 22.Use a² − b² = (a + b)(a − b) to find 68² − 67².
23. 23.Use a² − b² = (a + b)(a − b) to find 27² − 18².
24. 24.Use (a + b)² = a² + 2ab + b² to find 105².
25. 25.Use a² − b² = (a + b)(a − b) to find 76² − 8².
26. 26.Use (a − b)² = a² − 2ab + b² to find 27².
27. 27.Use (a − b)² = a² − 2ab + b² to find 13².
28. 28.Use (a + b)² = a² + 2ab + b² to find 32².
29. 29.If a − b = 6 and ab = 40, what is a² + b²?
30. 30.Find the value of x² − y² when x = 10 and y = 7.
31. 31.Use (a + b)² = a² + 2ab + b² to find 33².
32. 32.Find the value of x² − 2xy + y² when x = 5 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 17².
34. 34.Use a² − b² = (a + b)(a − b) to find 41² − 25².
35. 35.Use (a + b)(a − b) = a² − b² to find 32 × 28.
36. 36.If a − b = 3 and ab = 18, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 33² − 32².
38. 38.Use (a − b)² = a² − 2ab + b² to find 29².
39. 39.If a + b = 4 and ab = 3, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 47 × 33.

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