Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 31 · 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 57².
2. 2.Use (a + b)(a − b) = a² − b² to find 95 × 85.
3. 3.Use (a + b)² = a² + 2ab + b² to find 48².
4. 4.Use (a + b)(a − b) = a² − b² to find 107 × 93.
5. 5.Use (a + b)(a − b) = a² − b² to find 62 × 58.
6. 6.Use a² − b² = (a + b)(a − b) to find 81² − 49².
7. 7.Use (a + b)² = a² + 2ab + b² to find 101².
8. 8.Find the value of x² + 2xy + y² when x = 5 and y = 1.
9. 9.If a − b = 9 and ab = 36, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 51 × 49.
11. 11.Use (a − b)² = a² − 2ab + b² to find 98².
12. 12.Find the value of x² − 2xy + y² when x = 5 and y = 4.
13. 13.If a − b = 1 and ab = 20, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 76².
15. 15.If a + b = 10 and ab = 16, what is a² + b²?
16. 16.If a − b = 7 and ab = 8, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 49 × 31.
18. 18.If a − b = 1 and ab = 12, what is a² + b²?
19. 19.Find the value of x² − y² when x = 8 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 71².
21. 21.Find the value of x² − y² when x = 7 and y = 1.
22. 22.Use (a + b)² = a² + 2ab + b² to find 83².
23. 23.If a + b = 10 and ab = 9, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 81 × 79.
25. 25.Use a² − b² = (a + b)(a − b) to find 81² − 71².
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.If a + b = 11 and ab = 24, what is a² + b²?
28. 28.Find the value of x² − 2xy + y² when x = 5 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 27².
30. 30.Use (a + b)² = a² + 2ab + b² to find 22².
31. 31.Use a² − b² = (a + b)(a − b) to find 44² − 6².
32. 32.Use a² − b² = (a + b)(a − b) to find 37² − 33².
33. 33.Use (a − b)² = a² − 2ab + b² to find 61².
34. 34.If a + b = 9 and ab = 14, what is a² + b²?
35. 35.If a + b = 16 and ab = 48, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 69² − 66².
37. 37.Use (a + b)(a − b) = a² − b² to find 93 × 87.
38. 38.Use (a + b)² = a² + 2ab + b² to find 13².
39. 39.Use (a + b)² = a² + 2ab + b² to find 92².
40. 40.Use a² − b² = (a + b)(a − b) to find 25² − 8².

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