Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 96 · 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 66².
2. 2.Find the value of x² − y² when x = 7 and y = 3.
3. 3.Use (a + b)(a − b) = a² − b² to find 44 × 36.
4. 4.If a + b = 6 and ab = 5, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 58².
6. 6.Use (a + b)(a − b) = a² − b² to find 72 × 68.
7. 7.Find the value of x² − 2xy + y² when x = 14 and y = 3.
8. 8.If a − b = 10 and ab = 24, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 25².
10. 10.Use (a + b)² = a² + 2ab + b² to find 61².
11. 11.If a − b = 3 and ab = 4, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 72².
13. 13.If a + b = 13 and ab = 36, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 32².
15. 15.Use (a + b)² = a² + 2ab + b² to find 78².
16. 16.Use (a − b)² = a² − 2ab + b² to find 49².
17. 17.If a − b = 3 and ab = 10, what is a² + b²?
18. 18.If a − b = 1 and ab = 6, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 96².
20. 20.Use (a + b)(a − b) = a² − b² to find 36 × 24.
21. 21.Use a² − b² = (a + b)(a − b) to find 31² − 19².
22. 22.Use (a + b)(a − b) = a² − b² to find 74 × 66.
23. 23.Find the value of x² − 2xy + y² when x = 11 and y = 2.
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 99² − 89².
26. 26.Use (a + b)² = a² + 2ab + b² to find 28².
27. 27.Use (a + b)(a − b) = a² − b² to find 94 × 86.
28. 28.Use (a + b)² = a² + 2ab + b² to find 23².
29. 29.Use (a + b)(a − b) = a² − b² to find 78 × 62.
30. 30.Use (a − b)² = a² − 2ab + b² to find 22².
31. 31.Use (a − b)² = a² − 2ab + b² to find 33².
32. 32.Use (a + b)(a − b) = a² − b² to find 43 × 37.
33. 33.If a + b = 12 and ab = 27, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 3 and y = 1.
35. 35.Use (a + b)² = a² + 2ab + b² to find 29².
36. 36.Use (a + b)² = a² + 2ab + b² to find 101².
37. 37.Use (a + b)² = a² + 2ab + b² to find 57².
38. 38.Use a² − b² = (a + b)(a − b) to find 98² − 76².
39. 39.Use (a − b)² = a² − 2ab + b² to find 57².
40. 40.If a + b = 12 and ab = 11, what is a² + b²?

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