Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 844 · 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.Find the value of x² − 2xy + y² when x = 11 and y = 10.
2. 2.Use (a + b)² = a² + 2ab + b² to find 21².
3. 3.Use (a + b)² = a² + 2ab + b² to find 89².
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 35².
6. 6.Use (a + b)² = a² + 2ab + b² to find 91².
7. 7.Use a² − b² = (a + b)(a − b) to find 61² − 21².
8. 8.Use a² − b² = (a + b)(a − b) to find 36² − 12².
9. 9.If a + b = 20 and ab = 96, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 38².
11. 11.If a + b = 16 and ab = 55, what is a² + b²?
12. 12.Find the value of x² − y² when x = 7 and y = 3.
13. 13.Use a² − b² = (a + b)(a − b) to find 33² − 29².
14. 14.Use (a + b)(a − b) = a² − b² to find 44 × 36.
15. 15.If a + b = 8 and ab = 7, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 11².
17. 17.Use (a − b)² = a² − 2ab + b² to find 66².
18. 18.Use (a − b)² = a² − 2ab + b² to find 72².
19. 19.Use (a + b)² = a² + 2ab + b² to find 22².
20. 20.Use (a + b)(a − b) = a² − b² to find 71 × 69.
21. 21.Use a² − b² = (a + b)(a − b) to find 84² − 66².
22. 22.Use (a − b)² = a² − 2ab + b² to find 39².
23. 23.Use a² − b² = (a + b)(a − b) to find 39² − 13².
24. 24.Use (a − b)² = a² − 2ab + b² to find 64².
25. 25.Use a² − b² = (a + b)(a − b) to find 57² − 28².
26. 26.Use (a + b)² = a² + 2ab + b² to find 98².
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 3.
28. 28.Use (a − b)² = a² − 2ab + b² to find 83².
29. 29.Use a² − b² = (a + b)(a − b) to find 78² − 72².
30. 30.Use (a + b)(a − b) = a² − b² to find 49 × 31.
31. 31.Use (a + b)² = a² + 2ab + b² to find 26².
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.Use (a + b)(a − b) = a² − b² to find 93 × 87.
34. 34.If a − b = 3 and ab = 10, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 26² − 11².
36. 36.Use (a + b)² = a² + 2ab + b² to find 17².
37. 37.Find the value of x² + 2xy + y² when x = 6 and y = 3.
38. 38.Use (a − b)² = a² − 2ab + b² to find 93².
39. 39.Use a² − b² = (a + b)(a − b) to find 49² − 9².
40. 40.Use (a − b)² = a² − 2ab + b² to find 97².

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