Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 773 · 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 − y² when x = 13 and y = 1.
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 49².
4. 4.If a − b = 1 and ab = 6, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 35² − 8².
6. 6.Use (a + b)² = a² + 2ab + b² to find 81².
7. 7.Use (a + b)² = a² + 2ab + b² to find 36².
8. 8.Find the value of x² − y² when x = 8 and y = 3.
9. 9.Use a² − b² = (a + b)(a − b) to find 38² − 10².
10. 10.Use (a − b)² = a² − 2ab + b² to find 87².
11. 11.Find the value of x² − y² when x = 6 and y = 3.
12. 12.Find the value of x² − y² when x = 10 and y = 7.
13. 13.Use (a − b)² = a² − 2ab + b² to find 82².
14. 14.Use (a + b)² = a² + 2ab + b² to find 84².
15. 15.Use (a + b)² = a² + 2ab + b² to find 58².
16. 16.Find the value of x² − 2xy + y² when x = 6 and y = 5.
17. 17.Use (a + b)² = a² + 2ab + b² to find 97².
18. 18.Use (a + b)(a − b) = a² − b² to find 66 × 54.
19. 19.Use a² − b² = (a + b)(a − b) to find 28² − 19².
20. 20.Use (a + b)(a − b) = a² − b² to find 29 × 11.
21. 21.Use (a + b)(a − b) = a² − b² to find 83 × 77.
22. 22.Use (a + b)(a − b) = a² − b² to find 74 × 66.
23. 23.If a − b = 2 and ab = 3, what is a² + b²?
24. 24.If a + b = 17 and ab = 72, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 38² − 15².
26. 26.Use (a − b)² = a² − 2ab + b² to find 84².
27. 27.Use (a − b)² = a² − 2ab + b² to find 57².
28. 28.Use (a − b)² = a² − 2ab + b² to find 18².
29. 29.If a + b = 5 and ab = 4, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 42 × 38.
31. 31.Use a² − b² = (a + b)(a − b) to find 20² − 11².
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 91² − 20².
34. 34.Use a² − b² = (a + b)(a − b) to find 80² − 71².
35. 35.Use a² − b² = (a + b)(a − b) to find 26² − 16².
36. 36.If a + b = 6 and ab = 5, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 55² − 21².
38. 38.Find the value of x² + 2xy + y² when x = 11 and y = 8.
39. 39.Use a² − b² = (a + b)(a − b) to find 66² − 11².
40. 40.Use (a + b)² = a² + 2ab + b² to find 39².

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