Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 549 · 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 (a − b)² = a² − 2ab + b² to find 81².
2. 2.If a + b = 9 and ab = 20, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 97².
4. 4.Use (a + b)² = a² + 2ab + b² to find 68².
5. 5.Use (a − b)² = a² − 2ab + b² to find 17².
6. 6.If a − b = 3 and ab = 4, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 103 × 97.
8. 8.If a + b = 3 and ab = 2, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 98².
10. 10.Use (a + b)(a − b) = a² − b² to find 29 × 11.
11. 11.Use (a + b)² = a² + 2ab + b² to find 92².
12. 12.Use (a + b)(a − b) = a² − b² to find 69 × 51.
13. 13.Find the value of x² − 2xy + y² when x = 7 and y = 3.
14. 14.Use (a + b)(a − b) = a² − b² to find 53 × 47.
15. 15.Use (a + b)(a − b) = a² − b² to find 78 × 62.
16. 16.If a + b = 6 and ab = 5, what is a² + b²?
17. 17.Find the value of x² − y² when x = 11 and y = 4.
18. 18.If a − b = 1 and ab = 20, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 93² − 57².
20. 20.Use (a − b)² = a² − 2ab + b² to find 18².
21. 21.Use (a − b)² = a² − 2ab + b² to find 49².
22. 22.Use (a + b)² = a² + 2ab + b² to find 61².
23. 23.Use (a + b)(a − b) = a² − b² to find 105 × 95.
24. 24.If a − b = 2 and ab = 63, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 99² − 24².
26. 26.Use a² − b² = (a + b)(a − b) to find 94² − 13².
27. 27.Use (a + b)(a − b) = a² − b² to find 58 × 42.
28. 28.Use a² − b² = (a + b)(a − b) to find 22² − 4².
29. 29.Use (a + b)(a − b) = a² − b² to find 42 × 38.
30. 30.Use (a + b)² = a² + 2ab + b² to find 39².
31. 31.If a − b = 2 and ab = 120, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 22².
33. 33.Use (a + b)² = a² + 2ab + b² to find 109².
34. 34.Use (a − b)² = a² − 2ab + b² to find 67².
35. 35.Find the value of x² − y² when x = 7 and y = 1.
36. 36.If a + b = 8 and ab = 7, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 94².
38. 38.Use a² − b² = (a + b)(a − b) to find 46² − 6².
39. 39.If a − b = 4 and ab = 5, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 3 and y = 1.

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