Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 463 · 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 23².
2. 2.Use (a − b)² = a² − 2ab + b² to find 42².
3. 3.Use (a − b)² = a² − 2ab + b² to find 28².
4. 4.Use (a + b)² = a² + 2ab + b² to find 82².
5. 5.Use (a + b)(a − b) = a² − b² to find 68 × 52.
6. 6.Find the value of x² − 2xy + y² when x = 6 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 57 × 43.
8. 8.Find the value of x² + 2xy + y² when x = 12 and y = 2.
9. 9.If a − b = 2 and ab = 15, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 34².
11. 11.Find the value of x² − y² when x = 9 and y = 5.
12. 12.Use a² − b² = (a + b)(a − b) to find 78² − 15².
13. 13.Use (a − b)² = a² − 2ab + b² to find 76².
14. 14.Use (a + b)(a − b) = a² − b² to find 41 × 39.
15. 15.Find the value of x² − y² when x = 5 and y = 4.
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 3 and y = 1.
18. 18.If a − b = 1 and ab = 20, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 21².
20. 20.Find the value of x² + 2xy + y² when x = 10 and y = 5.
21. 21.Use (a + b)(a − b) = a² − b² to find 24 × 16.
22. 22.Use (a − b)² = a² − 2ab + b² to find 16².
23. 23.Use a² − b² = (a + b)(a − b) to find 75² − 65².
24. 24.Use a² − b² = (a + b)(a − b) to find 75² − 34².
25. 25.Use (a − b)² = a² − 2ab + b² to find 17².
26. 26.Use a² − b² = (a + b)(a − b) to find 97² − 39².
27. 27.If a + b = 22 and ab = 120, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 25².
29. 29.Use (a + b)² = a² + 2ab + b² to find 36².
30. 30.Use (a + b)² = a² + 2ab + b² to find 22².
31. 31.Use (a + b)² = a² + 2ab + b² to find 27².
32. 32.Use (a + b)² = a² + 2ab + b² to find 49².
33. 33.If a + b = 11 and ab = 24, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 24².
35. 35.Use (a − b)² = a² − 2ab + b² to find 97².
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.Use (a − b)² = a² − 2ab + b² to find 73².
38. 38.Use a² − b² = (a + b)(a − b) to find 82² − 43².
39. 39.Use (a − b)² = a² − 2ab + b² to find 51².
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 5.

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