Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 478 · 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.If a − b = 3 and ab = 54, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 76² − 68².
3. 3.Use (a − b)² = a² − 2ab + b² to find 89².
4. 4.Use (a + b)² = a² + 2ab + b² to find 36².
5. 5.Use a² − b² = (a + b)(a − b) to find 25² − 22².
6. 6.Use (a + b)² = a² + 2ab + b² to find 73².
7. 7.Use a² − b² = (a + b)(a − b) to find 81² − 49².
8. 8.Use (a − b)² = a² − 2ab + b² to find 38².
9. 9.Use a² − b² = (a + b)(a − b) to find 77² − 61².
10. 10.Find the value of x² − 2xy + y² when x = 10 and y = 6.
11. 11.Use (a − b)² = a² − 2ab + b² to find 66².
12. 12.Find the value of x² − y² when x = 5 and y = 4.
13. 13.Use (a + b)² = a² + 2ab + b² to find 71².
14. 14.Use (a + b)(a − b) = a² − b² to find 57 × 43.
15. 15.Use (a + b)² = a² + 2ab + b² to find 69².
16. 16.Use (a + b)(a − b) = a² − b² to find 106 × 94.
17. 17.Use a² − b² = (a + b)(a − b) to find 86² − 19².
18. 18.Use (a − b)² = a² − 2ab + b² to find 13².
19. 19.Find the value of x² + 2xy + y² when x = 6 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 57² − 18².
21. 21.Use (a + b)² = a² + 2ab + b² to find 89².
22. 22.Use (a + b)(a − b) = a² − b² to find 34 × 26.
23. 23.Use (a + b)² = a² + 2ab + b² to find 103².
24. 24.Use (a − b)² = a² − 2ab + b² to find 94².
25. 25.If a + b = 15 and ab = 56, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 15².
27. 27.Use (a + b)² = a² + 2ab + b² to find 46².
28. 28.Use (a + b)(a − b) = a² − b² to find 67 × 53.
29. 29.Use a² − b² = (a + b)(a − b) to find 90² − 72².
30. 30.Use (a − b)² = a² − 2ab + b² to find 69².
31. 31.Use (a − b)² = a² − 2ab + b² to find 15².
32. 32.If a + b = 13 and ab = 30, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 38 × 22.
34. 34.Find the value of x² + 2xy + y² when x = 11 and y = 6.
35. 35.Use a² − b² = (a + b)(a − b) to find 77² − 59².
36. 36.If a + b = 3 and ab = 2, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 86².
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.Use a² − b² = (a + b)(a − b) to find 44² − 7².
40. 40.Use a² − b² = (a + b)(a − b) to find 93² − 8².

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