Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 829 · 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 = 15 and y = 12.
2. 2.If a − b = 6 and ab = 16, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 96².
4. 4.Use (a + b)² = a² + 2ab + b² to find 52².
5. 5.Use (a + b)² = a² + 2ab + b² to find 17².
6. 6.If a + b = 12 and ab = 35, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 42².
8. 8.Use (a + b)(a − b) = a² − b² to find 35 × 25.
9. 9.Find the value of x² − y² when x = 14 and y = 8.
10. 10.If a + b = 18 and ab = 77, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 81².
12. 12.Use (a + b)² = a² + 2ab + b² to find 38².
13. 13.If a + b = 7 and ab = 6, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 28².
15. 15.Use (a + b)(a − b) = a² − b² to find 45 × 35.
16. 16.Use a² − b² = (a + b)(a − b) to find 37² − 23².
17. 17.If a + b = 18 and ab = 80, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 73².
19. 19.Use (a + b)² = a² + 2ab + b² to find 49².
20. 20.Use a² − b² = (a + b)(a − b) to find 87² − 76².
21. 21.Use a² − b² = (a + b)(a − b) to find 50² − 17².
22. 22.Use (a + b)² = a² + 2ab + b² to find 33².
23. 23.Use (a − b)² = a² − 2ab + b² to find 29².
24. 24.Find the value of x² − y² when x = 8 and y = 5.
25. 25.Use (a + b)(a − b) = a² − b² to find 28 × 12.
26. 26.Use a² − b² = (a + b)(a − b) to find 98² − 75².
27. 27.Find the value of x² + 2xy + y² when x = 8 and y = 1.
28. 28.Use (a + b)(a − b) = a² − b² to find 27 × 13.
29. 29.Use (a + b)(a − b) = a² − b² to find 94 × 86.
30. 30.Use (a + b)² = a² + 2ab + b² to find 23².
31. 31.Use (a + b)(a − b) = a² − b² to find 59 × 41.
32. 32.Use (a − b)² = a² − 2ab + b² to find 35².
33. 33.Use (a + b)² = a² + 2ab + b² to find 79².
34. 34.Use (a + b)(a − b) = a² − b² to find 69 × 51.
35. 35.If a − b = 1 and ab = 20, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 19².
37. 37.Use a² − b² = (a + b)(a − b) to find 89² − 66².
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Find the value of x² − y² when x = 12 and y = 1.
40. 40.If a − b = 9 and ab = 36, what is a² + b²?

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