Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 396 · 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 = 4 and ab = 3, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 33².
3. 3.Use (a − b)² = a² − 2ab + b² to find 68².
4. 4.Use a² − b² = (a + b)(a − b) to find 26² − 19².
5. 5.Use (a + b)² = a² + 2ab + b² to find 64².
6. 6.Use (a + b)(a − b) = a² − b² to find 76 × 64.
7. 7.Use (a + b)(a − b) = a² − b² to find 38 × 22.
8. 8.Use a² − b² = (a + b)(a − b) to find 66² − 23².
9. 9.Use (a + b)(a − b) = a² − b² to find 55 × 45.
10. 10.Use (a + b)(a − b) = a² − b² to find 103 × 97.
11. 11.Use a² − b² = (a + b)(a − b) to find 32² − 24².
12. 12.Use (a + b)² = a² + 2ab + b² to find 83².
13. 13.Use (a + b)² = a² + 2ab + b² to find 82².
14. 14.Use (a − b)² = a² − 2ab + b² to find 43².
15. 15.Use a² − b² = (a + b)(a − b) to find 61² − 17².
16. 16.Use (a + b)(a − b) = a² − b² to find 74 × 66.
17. 17.Use (a − b)² = a² − 2ab + b² to find 32².
18. 18.If a − b = 8 and ab = 20, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 6 and y = 2.
20. 20.Use (a − b)² = a² − 2ab + b² to find 19².
21. 21.If a − b = 2 and ab = 8, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 48 × 32.
23. 23.Use a² − b² = (a + b)(a − b) to find 84² − 12².
24. 24.Use (a + b)² = a² + 2ab + b² to find 105².
25. 25.Use (a − b)² = a² − 2ab + b² to find 39².
26. 26.Use a² − b² = (a + b)(a − b) to find 24² − 16².
27. 27.If a + b = 15 and ab = 54, what is a² + b²?
28. 28.If a + b = 13 and ab = 12, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 1².
30. 30.Use (a + b)(a − b) = a² − b² to find 81 × 79.
31. 31.If a − b = 3 and ab = 18, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 102 × 98.
33. 33.If a − b = 3 and ab = 70, what is a² + b²?
34. 34.If a − b = 3 and ab = 4, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 76².
36. 36.Use (a + b)² = a² + 2ab + b² to find 11².
37. 37.Use (a + b)² = a² + 2ab + b² to find 87².
38. 38.If a − b = 2 and ab = 80, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 63².
40. 40.If a − b = 5 and ab = 6, what is a² + b²?

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