Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 702 · 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 − 2xy + y² when x = 8 and y = 7.
2. 2.Use (a − b)² = a² − 2ab + b² to find 34².
3. 3.If a + b = 10 and ab = 24, what is a² + b²?
4. 4.Find the value of x² − y² when x = 5 and y = 3.
5. 5.Use (a + b)² = a² + 2ab + b² to find 18².
6. 6.Use (a + b)² = a² + 2ab + b² to find 54².
7. 7.Use (a + b)² = a² + 2ab + b² to find 46².
8. 8.Use a² − b² = (a + b)(a − b) to find 48² − 24².
9. 9.Use (a − b)² = a² − 2ab + b² to find 74².
10. 10.Find the value of x² − y² when x = 13 and y = 11.
11. 11.Use (a + b)(a − b) = a² − b² to find 99 × 81.
12. 12.Use a² − b² = (a + b)(a − b) to find 73² − 57².
13. 13.Use a² − b² = (a + b)(a − b) to find 94² − 13².
14. 14.Use (a + b)(a − b) = a² − b² to find 82 × 78.
15. 15.Use (a + b)(a − b) = a² − b² to find 48 × 32.
16. 16.Use (a − b)² = a² − 2ab + b² to find 85².
17. 17.Use a² − b² = (a + b)(a − b) to find 86² − 26².
18. 18.If a + b = 4 and ab = 3, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 15².
20. 20.Find the value of x² − y² when x = 5 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 49².
22. 22.Use (a + b)² = a² + 2ab + b² to find 63².
23. 23.Use a² − b² = (a + b)(a − b) to find 26² − 14².
24. 24.Use (a + b)² = a² + 2ab + b² to find 69².
25. 25.Use a² − b² = (a + b)(a − b) to find 30² − 27².
26. 26.Use a² − b² = (a + b)(a − b) to find 76² − 15².
27. 27.Use (a + b)² = a² + 2ab + b² to find 23².
28. 28.Use (a − b)² = a² − 2ab + b² to find 23².
29. 29.Use (a + b)² = a² + 2ab + b² to find 88².
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 28².
32. 32.Use a² − b² = (a + b)(a − b) to find 47² − 45².
33. 33.Use (a + b)(a − b) = a² − b² to find 51 × 49.
34. 34.Use a² − b² = (a + b)(a − b) to find 39² − 5².
35. 35.Use (a − b)² = a² − 2ab + b² to find 96².
36. 36.Use (a + b)² = a² + 2ab + b² to find 109².
37. 37.Use (a + b)(a − b) = a² − b² to find 66 × 54.
38. 38.If a − b = 1 and ab = 56, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 13².
40. 40.Use a² − b² = (a + b)(a − b) to find 73² − 35².

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