Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 645 · 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.If a + b = 15 and ab = 50, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 15 and y = 4.
3. 3.If a − b = 2 and ab = 35, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 20² − 15².
5. 5.Use (a + b)² = a² + 2ab + b² to find 74².
6. 6.If a − b = 9 and ab = 10, what is a² + b²?
7. 7.If a − b = 6 and ab = 7, what is a² + b²?
8. 8.If a − b = 4 and ab = 32, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 59 × 41.
10. 10.Use (a + b)² = a² + 2ab + b² to find 53².
11. 11.Use (a + b)(a − b) = a² − b² to find 104 × 96.
12. 12.Use (a − b)² = a² − 2ab + b² to find 99².
13. 13.Use (a + b)² = a² + 2ab + b² to find 51².
14. 14.Find the value of x² − y² when x = 3 and y = 2.
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 75².
17. 17.Use a² − b² = (a + b)(a − b) to find 74² − 28².
18. 18.Use a² − b² = (a + b)(a − b) to find 50² − 10².
19. 19.Use (a + b)² = a² + 2ab + b² to find 31².
20. 20.If a − b = 5 and ab = 14, what is a² + b²?
21. 21.If a − b = 3 and ab = 108, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 84² − 52².
23. 23.Use (a + b)² = a² + 2ab + b² to find 28².
24. 24.If a + b = 18 and ab = 80, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 15².
26. 26.If a − b = 5 and ab = 66, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 81 × 79.
28. 28.Use (a + b)(a − b) = a² − b² to find 58 × 42.
29. 29.Use (a + b)(a − b) = a² − b² to find 54 × 46.
30. 30.Find the value of x² + 2xy + y² when x = 4 and y = 3.
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.Use (a − b)² = a² − 2ab + b² to find 15².
33. 33.Use (a + b)² = a² + 2ab + b² to find 57².
34. 34.Use (a − b)² = a² − 2ab + b² to find 26².
35. 35.Use a² − b² = (a + b)(a − b) to find 61² − 13².
36. 36.Use (a + b)² = a² + 2ab + b² to find 49².
37. 37.Use (a + b)² = a² + 2ab + b² to find 62².
38. 38.Use (a + b)(a − b) = a² − b² to find 31 × 29.
39. 39.Use a² − b² = (a + b)(a − b) to find 61² − 60².
40. 40.Find the value of x² + 2xy + y² when x = 6 and y = 5.

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