Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 415 · 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 88².
2. 2.Use (a − b)² = a² − 2ab + b² to find 22².
3. 3.Use (a + b)(a − b) = a² − b² to find 32 × 28.
4. 4.Use (a + b)² = a² + 2ab + b² to find 92².
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.Use (a + b)² = a² + 2ab + b² to find 46².
8. 8.If a + b = 20 and ab = 96, what is a² + b²?
9. 9.If a + b = 8 and ab = 15, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 63².
11. 11.If a − b = 4 and ab = 5, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 41² − 3².
13. 13.Find the value of x² − y² when x = 11 and y = 9.
14. 14.Use (a − b)² = a² − 2ab + b² to find 17².
15. 15.Use (a − b)² = a² − 2ab + b² to find 91².
16. 16.Use (a + b)² = a² + 2ab + b² to find 14².
17. 17.Use (a + b)(a − b) = a² − b² to find 103 × 97.
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 74² − 10².
20. 20.Use (a − b)² = a² − 2ab + b² to find 47².
21. 21.Use (a − b)² = a² − 2ab + b² to find 65².
22. 22.Use (a − b)² = a² − 2ab + b² to find 15².
23. 23.Use (a − b)² = a² − 2ab + b² to find 27².
24. 24.Find the value of x² − y² when x = 9 and y = 4.
25. 25.Use (a + b)² = a² + 2ab + b² to find 52².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 49².
28. 28.Find the value of x² + 2xy + y² when x = 4 and y = 3.
29. 29.Use (a + b)(a − b) = a² − b² to find 83 × 77.
30. 30.Use a² − b² = (a + b)(a − b) to find 30² − 17².
31. 31.Use (a − b)² = a² − 2ab + b² to find 52².
32. 32.Use (a − b)² = a² − 2ab + b² to find 28².
33. 33.Use (a + b)(a − b) = a² − b² to find 102 × 98.
34. 34.Use (a + b)² = a² + 2ab + b² to find 54².
35. 35.Use a² − b² = (a + b)(a − b) to find 86² − 53².
36. 36.If a + b = 9 and ab = 20, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 18².
38. 38.Use a² − b² = (a + b)(a − b) to find 63² − 24².
39. 39.Use (a + b)² = a² + 2ab + b² to find 66².
40. 40.Use (a + b)(a − b) = a² − b² to find 99 × 81.

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