Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 978 · 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 a² − b² = (a + b)(a − b) to find 97² − 72².
2. 2.Use a² − b² = (a + b)(a − b) to find 27² − 5².
3. 3.Use (a − b)² = a² − 2ab + b² to find 17².
4. 4.Use (a + b)(a − b) = a² − b² to find 29 × 11.
5. 5.If a + b = 5 and ab = 6, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 33².
7. 7.Find the value of x² − 2xy + y² when x = 14 and y = 9.
8. 8.Find the value of x² + 2xy + y² when x = 7 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 93 × 87.
10. 10.If a + b = 12 and ab = 11, what is a² + b²?
11. 11.If a + b = 13 and ab = 36, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 93².
13. 13.Use a² − b² = (a + b)(a − b) to find 53² − 49².
14. 14.Use (a − b)² = a² − 2ab + b² to find 23².
15. 15.If a − b = 1 and ab = 2, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 95 × 85.
17. 17.Find the value of x² + 2xy + y² when x = 8 and y = 2.
18. 18.Use (a + b)² = a² + 2ab + b² to find 109².
19. 19.Use (a + b)² = a² + 2ab + b² to find 52².
20. 20.Use (a − b)² = a² − 2ab + b² to find 27².
21. 21.Use (a − b)² = a² − 2ab + b² to find 82².
22. 22.Use (a + b)² = a² + 2ab + b² to find 86².
23. 23.Use (a + b)² = a² + 2ab + b² to find 53².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 81 × 79.
26. 26.Find the value of x² − 2xy + y² when x = 10 and y = 9.
27. 27.Use a² − b² = (a + b)(a − b) to find 54² − 15².
28. 28.Use (a + b)² = a² + 2ab + b² to find 32².
29. 29.If a − b = 3 and ab = 28, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 93² − 74².
31. 31.Find the value of x² − 2xy + y² when x = 15 and y = 14.
32. 32.Use a² − b² = (a + b)(a − b) to find 67² − 46².
33. 33.Find the value of x² + 2xy + y² when x = 10 and y = 6.
34. 34.Use (a + b)² = a² + 2ab + b² to find 69².
35. 35.Find the value of x² − y² when x = 8 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 96².
37. 37.Use a² − b² = (a + b)(a − b) to find 29² − 10².
38. 38.If a + b = 10 and ab = 24, what is a² + b²?
39. 39.If a + b = 6 and ab = 8, what is a² + b²?
40. 40.Find the value of x² − y² when x = 3 and y = 1.

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