Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 826 · 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 = 8.
2. 2.Use a² − b² = (a + b)(a − b) to find 84² − 21².
3. 3.Use a² − b² = (a + b)(a − b) to find 62² − 53².
4. 4.Find the value of x² + 2xy + y² when x = 12 and y = 7.
5. 5.If a − b = 2 and ab = 8, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 31².
7. 7.Use (a − b)² = a² − 2ab + b² to find 29².
8. 8.Use a² − b² = (a + b)(a − b) to find 56² − 44².
9. 9.Use a² − b² = (a + b)(a − b) to find 50² − 30².
10. 10.Use a² − b² = (a + b)(a − b) to find 21² − 19².
11. 11.Use (a + b)(a − b) = a² − b² to find 81 × 79.
12. 12.Use (a − b)² = a² − 2ab + b² to find 22².
13. 13.Find the value of x² − 2xy + y² when x = 13 and y = 12.
14. 14.Use a² − b² = (a + b)(a − b) to find 60² − 15².
15. 15.Use (a + b)² = a² + 2ab + b² to find 98².
16. 16.Use (a + b)² = a² + 2ab + b² to find 79².
17. 17.Use (a + b)² = a² + 2ab + b² to find 95².
18. 18.Use (a + b)² = a² + 2ab + b² to find 62².
19. 19.Find the value of x² − 2xy + y² when x = 9 and y = 5.
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Use (a + b)² = a² + 2ab + b² to find 44².
22. 22.Find the value of x² − y² when x = 3 and y = 1.
23. 23.Use (a + b)² = a² + 2ab + b² to find 61².
24. 24.Use (a − b)² = a² − 2ab + b² to find 12².
25. 25.Use a² − b² = (a + b)(a − b) to find 67² − 54².
26. 26.Use (a − b)² = a² − 2ab + b² to find 27².
27. 27.If a + b = 5 and ab = 6, what is a² + b²?
28. 28.Find the value of x² − y² when x = 10 and y = 5.
29. 29.If a + b = 9 and ab = 20, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 57².
31. 31.Use a² − b² = (a + b)(a − b) to find 26² − 7².
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 1.
33. 33.Use (a − b)² = a² − 2ab + b² to find 62².
34. 34.Use (a + b)(a − b) = a² − b² to find 39 × 21.
35. 35.Find the value of x² − y² when x = 13 and y = 2.
36. 36.Use a² − b² = (a + b)(a − b) to find 82² − 73².
37. 37.Use a² − b² = (a + b)(a − b) to find 86² − 12².
38. 38.If a − b = 5 and ab = 50, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 55 × 45.
40. 40.If a + b = 11 and ab = 30, what is a² + b²?

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