Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 184 · 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 89² − 60².
2. 2.Use a² − b² = (a + b)(a − b) to find 37² − 5².
3. 3.Use (a + b)² = a² + 2ab + b² to find 81².
4. 4.Use (a − b)² = a² − 2ab + b² to find 45².
5. 5.Use a² − b² = (a + b)(a − b) to find 20² − 2².
6. 6.Find the value of x² + 2xy + y² when x = 13 and y = 11.
7. 7.Use (a + b)² = a² + 2ab + b² to find 97².
8. 8.Use (a − b)² = a² − 2ab + b² to find 81².
9. 9.Use (a + b)² = a² + 2ab + b² to find 47².
10. 10.If a − b = 7 and ab = 30, what is a² + b²?
11. 11.If a + b = 5 and ab = 4, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 107².
13. 13.If a − b = 4 and ab = 5, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 87² − 13².
15. 15.Use (a + b)(a − b) = a² − b² to find 34 × 26.
16. 16.Use (a − b)² = a² − 2ab + b² to find 35².
17. 17.Use (a − b)² = a² − 2ab + b² to find 49².
18. 18.Find the value of x² − y² when x = 10 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 78².
20. 20.Use (a + b)² = a² + 2ab + b² to find 102².
21. 21.Use (a − b)² = a² − 2ab + b² to find 31².
22. 22.Use (a + b)² = a² + 2ab + b² to find 87².
23. 23.Use (a + b)² = a² + 2ab + b² to find 74².
24. 24.Use (a + b)² = a² + 2ab + b² to find 51².
25. 25.Use a² − b² = (a + b)(a − b) to find 93² − 21².
26. 26.If a − b = 8 and ab = 9, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 54 × 46.
28. 28.If a + b = 12 and ab = 35, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 65² − 16².
30. 30.If a − b = 7 and ab = 18, what is a² + b²?
31. 31.If a − b = 3 and ab = 10, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 26².
33. 33.Use (a + b)² = a² + 2ab + b² to find 31².
34. 34.Use (a + b)² = a² + 2ab + b² to find 67².
35. 35.Use a² − b² = (a + b)(a − b) to find 40² − 19².
36. 36.Use (a − b)² = a² − 2ab + b² to find 62².
37. 37.If a + b = 4 and ab = 3, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 91².
39. 39.Use a² − b² = (a + b)(a − b) to find 99² − 9².
40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 2.

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