Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 754 · 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 87².
2. 2.Use (a − b)² = a² − 2ab + b² to find 71².
3. 3.Find the value of x² − y² when x = 14 and y = 11.
4. 4.Find the value of x² − 2xy + y² when x = 6 and y = 1.
5. 5.Use (a + b)² = a² + 2ab + b² to find 103².
6. 6.Use (a + b)² = a² + 2ab + b² to find 53².
7. 7.Use (a + b)(a − b) = a² − b² to find 82 × 78.
8. 8.Use (a + b)(a − b) = a² − b² to find 66 × 54.
9. 9.Use (a + b)(a − b) = a² − b² to find 35 × 25.
10. 10.Use a² − b² = (a + b)(a − b) to find 31² − 23².
11. 11.Use (a + b)(a − b) = a² − b² to find 57 × 43.
12. 12.Use a² − b² = (a + b)(a − b) to find 42² − 30².
13. 13.If a + b = 10 and ab = 16, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 83².
15. 15.Use (a + b)(a − b) = a² − b² to find 51 × 49.
16. 16.Find the value of x² + 2xy + y² when x = 8 and y = 4.
17. 17.Find the value of x² − 2xy + y² when x = 6 and y = 4.
18. 18.Use a² − b² = (a + b)(a − b) to find 35² − 34².
19. 19.Use a² − b² = (a + b)(a − b) to find 80² − 25².
20. 20.Use a² − b² = (a + b)(a − b) to find 74² − 22².
21. 21.Find the value of x² − 2xy + y² when x = 3 and y = 2.
22. 22.Use a² − b² = (a + b)(a − b) to find 24² − 3².
23. 23.Use (a + b)(a − b) = a² − b² to find 101 × 99.
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 3.
25. 25.Use (a + b)(a − b) = a² − b² to find 31 × 29.
26. 26.Use (a + b)(a − b) = a² − b² to find 41 × 39.
27. 27.Use (a + b)(a − b) = a² − b² to find 28 × 12.
28. 28.Use (a + b)² = a² + 2ab + b² to find 41².
29. 29.Find the value of x² − y² when x = 9 and y = 7.
30. 30.Use a² − b² = (a + b)(a − b) to find 40² − 23².
31. 31.Use (a + b)² = a² + 2ab + b² to find 64².
32. 32.Use (a − b)² = a² − 2ab + b² to find 19².
33. 33.Use (a + b)(a − b) = a² − b² to find 65 × 55.
34. 34.Use (a − b)² = a² − 2ab + b² to find 95².
35. 35.Use a² − b² = (a + b)(a − b) to find 87² − 72².
36. 36.If a + b = 11 and ab = 24, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 45 × 35.
38. 38.Use (a + b)(a − b) = a² − b² to find 85 × 75.
39. 39.If a − b = 8 and ab = 33, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 1.

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