Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 616 · 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 + 2xy + y² when x = 6 and y = 5.
2. 2.Use (a + b)² = a² + 2ab + b² to find 66².
3. 3.Find the value of x² + 2xy + y² when x = 9 and y = 3.
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 27².
6. 6.If a + b = 4 and ab = 3, what is a² + b²?
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Find the value of x² − y² when x = 14 and y = 7.
9. 9.Find the value of x² − y² when x = 13 and y = 2.
10. 10.Use a² − b² = (a + b)(a − b) to find 61² − 44².
11. 11.Use (a + b)(a − b) = a² − b² to find 71 × 69.
12. 12.Use (a − b)² = a² − 2ab + b² to find 61².
13. 13.Use (a − b)² = a² − 2ab + b² to find 32².
14. 14.Use (a − b)² = a² − 2ab + b² to find 57².
15. 15.Use (a − b)² = a² − 2ab + b² to find 94².
16. 16.Use (a + b)(a − b) = a² − b² to find 41 × 39.
17. 17.Use (a + b)² = a² + 2ab + b² to find 33².
18. 18.Use (a + b)² = a² + 2ab + b² to find 71².
19. 19.Use (a − b)² = a² − 2ab + b² to find 69².
20. 20.Use (a + b)² = a² + 2ab + b² to find 96².
21. 21.Find the value of x² + 2xy + y² when x = 6 and y = 3.
22. 22.Use (a + b)² = a² + 2ab + b² to find 16².
23. 23.Use (a − b)² = a² − 2ab + b² to find 77².
24. 24.Use a² − b² = (a + b)(a − b) to find 29² − 24².
25. 25.Use (a + b)² = a² + 2ab + b² to find 81².
26. 26.Use a² − b² = (a + b)(a − b) to find 82² − 22².
27. 27.Use (a + b)(a − b) = a² − b² to find 35 × 25.
28. 28.Use (a + b)² = a² + 2ab + b² to find 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 18².
30. 30.Use (a + b)² = a² + 2ab + b² to find 59².
31. 31.If a + b = 10 and ab = 21, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 4.
33. 33.Use a² − b² = (a + b)(a − b) to find 92² − 25².
34. 34.If a + b = 7 and ab = 10, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 93².
36. 36.Use (a − b)² = a² − 2ab + b² to find 46².
37. 37.Use (a + b)(a − b) = a² − b² to find 85 × 75.
38. 38.Use a² − b² = (a + b)(a − b) to find 22² − 13².
39. 39.Find the value of x² − y² when x = 15 and y = 14.
40. 40.Use a² − b² = (a + b)(a − b) to find 80² − 65².

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