Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 523 · 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 95² − 2².
2. 2.Use (a − b)² = a² − 2ab + b² to find 63².
3. 3.Use a² − b² = (a + b)(a − b) to find 87² − 41².
4. 4.Use a² − b² = (a + b)(a − b) to find 43² − 28².
5. 5.Use (a − b)² = a² − 2ab + b² to find 93².
6. 6.Use a² − b² = (a + b)(a − b) to find 86² − 54².
7. 7.Use (a + b)² = a² + 2ab + b² to find 82².
8. 8.Find the value of x² − 2xy + y² when x = 4 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 59 × 41.
10. 10.Use a² − b² = (a + b)(a − b) to find 47² − 29².
11. 11.Use (a − b)² = a² − 2ab + b² to find 66².
12. 12.Use a² − b² = (a + b)(a − b) to find 59² − 44².
13. 13.Use (a + b)² = a² + 2ab + b² to find 76².
14. 14.Use (a − b)² = a² − 2ab + b² to find 46².
15. 15.Find the value of x² − y² when x = 10 and y = 9.
16. 16.Use (a + b)² = a² + 2ab + b² to find 22².
17. 17.Use (a − b)² = a² − 2ab + b² to find 69².
18. 18.If a − b = 8 and ab = 9, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 79² − 2².
20. 20.Find the value of x² − 2xy + y² when x = 5 and y = 4.
21. 21.If a + b = 10 and ab = 9, what is a² + b²?
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 3.
23. 23.Find the value of x² − y² when x = 5 and y = 3.
24. 24.Find the value of x² − 2xy + y² when x = 12 and y = 10.
25. 25.Use (a − b)² = a² − 2ab + b² to find 25².
26. 26.Use (a + b)² = a² + 2ab + b² to find 95².
27. 27.If a + b = 23 and ab = 132, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 41².
29. 29.Use a² − b² = (a + b)(a − b) to find 51² − 5².
30. 30.Find the value of x² + 2xy + y² when x = 3 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 37².
32. 32.Use (a + b)² = a² + 2ab + b² to find 62².
33. 33.Find the value of x² − y² when x = 11 and y = 2.
34. 34.Use (a − b)² = a² − 2ab + b² to find 19².
35. 35.Find the value of x² + 2xy + y² when x = 6 and y = 2.
36. 36.Use (a − b)² = a² − 2ab + b² to find 34².
37. 37.Use (a + b)² = a² + 2ab + b² to find 72².
38. 38.Use (a − b)² = a² − 2ab + b² to find 83².
39. 39.Use (a + b)(a − b) = a² − b² to find 75 × 65.
40. 40.Use (a + b)(a − b) = a² − b² to find 89 × 71.

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