Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 522 · 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 − y² when x = 12 and y = 8.
2. 2.If a + b = 7 and ab = 12, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 83².
4. 4.Use (a + b)² = a² + 2ab + b² to find 33².
5. 5.Find the value of x² − 2xy + y² when x = 8 and y = 1.
6. 6.If a + b = 13 and ab = 22, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 32².
8. 8.Use (a − b)² = a² − 2ab + b² to find 21².
9. 9.Use (a − b)² = a² − 2ab + b² to find 14².
10. 10.Use (a − b)² = a² − 2ab + b² to find 16².
11. 11.Use (a − b)² = a² − 2ab + b² to find 98².
12. 12.Use (a + b)(a − b) = a² − b² to find 51 × 49.
13. 13.Use (a − b)² = a² − 2ab + b² to find 55².
14. 14.Find the value of x² − 2xy + y² when x = 10 and y = 6.
15. 15.Use (a + b)(a − b) = a² − b² to find 91 × 89.
16. 16.Use (a + b)² = a² + 2ab + b² to find 107².
17. 17.Use (a − b)² = a² − 2ab + b² to find 59².
18. 18.Use a² − b² = (a + b)(a − b) to find 62² − 22².
19. 19.Use (a + b)(a − b) = a² − b² to find 54 × 46.
20. 20.Use a² − b² = (a + b)(a − b) to find 64² − 34².
21. 21.Use a² − b² = (a + b)(a − b) to find 70² − 26².
22. 22.Use (a + b)² = a² + 2ab + b² to find 95².
23. 23.Use a² − b² = (a + b)(a − b) to find 55² − 39².
24. 24.Use a² − b² = (a + b)(a − b) to find 89² − 71².
25. 25.Use (a + b)(a − b) = a² − b² to find 41 × 39.
26. 26.Use (a − b)² = a² − 2ab + b² to find 45².
27. 27.Use (a + b)² = a² + 2ab + b² to find 13².
28. 28.Find the value of x² + 2xy + y² when x = 14 and y = 13.
29. 29.If a − b = 1 and ab = 30, what is a² + b²?
30. 30.If a + b = 12 and ab = 27, what is a² + b²?
31. 31.Find the value of x² + 2xy + y² when x = 6 and y = 3.
32. 32.If a + b = 19 and ab = 84, what is a² + b²?
33. 33.If a + b = 6 and ab = 5, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 34².
35. 35.Use (a − b)² = a² − 2ab + b² to find 86².
36. 36.If a + b = 15 and ab = 54, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 49².
38. 38.Use (a + b)² = a² + 2ab + b² to find 25².
39. 39.Use a² − b² = (a + b)(a − b) to find 77² − 29².
40. 40.Use a² − b² = (a + b)(a − b) to find 65² − 47².

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