Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 654 · 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)(a − b) = a² − b² to find 69 × 51.
2. 2.If a + b = 15 and ab = 44, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 62 × 58.
4. 4.Find the value of x² + 2xy + y² when x = 11 and y = 2.
5. 5.Use (a − b)² = a² − 2ab + b² to find 15².
6. 6.Use a² − b² = (a + b)(a − b) to find 42² − 28².
7. 7.Use (a + b)(a − b) = a² − b² to find 41 × 39.
8. 8.Use (a + b)² = a² + 2ab + b² to find 58².
9. 9.Use (a − b)² = a² − 2ab + b² to find 18².
10. 10.Use a² − b² = (a + b)(a − b) to find 57² − 19².
11. 11.Use (a + b)² = a² + 2ab + b² to find 23².
12. 12.Use (a − b)² = a² − 2ab + b² to find 41².
13. 13.If a − b = 1 and ab = 2, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 51².
15. 15.Use (a − b)² = a² − 2ab + b² to find 67².
16. 16.Use a² − b² = (a + b)(a − b) to find 80² − 53².
17. 17.Use (a − b)² = a² − 2ab + b² to find 34².
18. 18.If a − b = 5 and ab = 6, what is a² + b²?
19. 19.If a − b = 2 and ab = 3, what is a² + b²?
20. 20.If a − b = 2 and ab = 99, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 22².
22. 22.Use (a + b)² = a² + 2ab + b² to find 39².
23. 23.Use a² − b² = (a + b)(a − b) to find 44² − 35².
24. 24.Use (a + b)² = a² + 2ab + b² to find 72².
25. 25.Find the value of x² − 2xy + y² when x = 9 and y = 3.
26. 26.Use a² − b² = (a + b)(a − b) to find 91² − 23².
27. 27.Use (a + b)(a − b) = a² − b² to find 49 × 31.
28. 28.Use (a + b)(a − b) = a² − b² to find 48 × 32.
29. 29.Find the value of x² − 2xy + y² when x = 13 and y = 2.
30. 30.Use (a − b)² = a² − 2ab + b² to find 83².
31. 31.Use (a + b)² = a² + 2ab + b² to find 13².
32. 32.Use a² − b² = (a + b)(a − b) to find 98² − 88².
33. 33.If a + b = 15 and ab = 54, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 109 × 91.
35. 35.Use (a + b)(a − b) = a² − b² to find 29 × 11.
36. 36.Use (a + b)² = a² + 2ab + b² to find 68².
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 8.
38. 38.Use (a − b)² = a² − 2ab + b² to find 11².
39. 39.Use (a + b)(a − b) = a² − b² to find 63 × 57.
40. 40.Use (a + b)(a − b) = a² − b² to find 57 × 43.

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