Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 85 · 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 105².
2. 2.Use (a − b)² = a² − 2ab + b² to find 84².
3. 3.Use (a + b)² = a² + 2ab + b² to find 71².
4. 4.Use a² − b² = (a + b)(a − b) to find 24² − 7².
5. 5.Use (a − b)² = a² − 2ab + b² to find 39².
6. 6.Use (a − b)² = a² − 2ab + b² to find 78².
7. 7.If a − b = 2 and ab = 3, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 51 × 49.
9. 9.Use (a − b)² = a² − 2ab + b² to find 18².
10. 10.Use (a + b)(a − b) = a² − b² to find 34 × 26.
11. 11.Use (a + b)² = a² + 2ab + b² to find 28².
12. 12.Use (a − b)² = a² − 2ab + b² to find 59².
13. 13.Use (a + b)² = a² + 2ab + b² to find 61².
14. 14.Use (a − b)² = a² − 2ab + b² to find 16².
15. 15.Use (a − b)² = a² − 2ab + b² to find 71².
16. 16.Use a² − b² = (a + b)(a − b) to find 96² − 4².
17. 17.Use (a + b)² = a² + 2ab + b² to find 75².
18. 18.Find the value of x² + 2xy + y² when x = 3 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 33² − 6².
20. 20.If a + b = 5 and ab = 6, what is a² + b²?
21. 21.Find the value of x² − y² when x = 4 and y = 2.
22. 22.Use (a − b)² = a² − 2ab + b² to find 37².
23. 23.Use (a + b)(a − b) = a² − b² to find 54 × 46.
24. 24.Find the value of x² + 2xy + y² when x = 10 and y = 6.
25. 25.Use (a + b)(a − b) = a² − b² to find 46 × 34.
26. 26.Find the value of x² − 2xy + y² when x = 6 and y = 5.
27. 27.Use a² − b² = (a + b)(a − b) to find 77² − 28².
28. 28.Use a² − b² = (a + b)(a − b) to find 26² − 10².
29. 29.Use (a − b)² = a² − 2ab + b² to find 35².
30. 30.Find the value of x² − y² when x = 13 and y = 6.
31. 31.Use (a + b)² = a² + 2ab + b² to find 52².
32. 32.Find the value of x² − 2xy + y² when x = 10 and y = 5.
33. 33.Use (a + b)(a − b) = a² − b² to find 57 × 43.
34. 34.Use (a + b)² = a² + 2ab + b² to find 23².
35. 35.Use (a + b)(a − b) = a² − b² to find 109 × 91.
36. 36.Use (a + b)(a − b) = a² − b² to find 91 × 89.
37. 37.Use a² − b² = (a + b)(a − b) to find 34² − 7².
38. 38.If a − b = 2 and ab = 8, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 32² − 23².
40. 40.Find the value of x² − y² when x = 14 and y = 9.

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