Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 236 · 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 87².
2. 2.Use (a + b)(a − b) = a² − b² to find 52 × 48.
3. 3.Use (a + b)² = a² + 2ab + b² to find 43².
4. 4.Use (a + b)(a − b) = a² − b² to find 72 × 68.
5. 5.If a − b = 1 and ab = 2, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 23 × 17.
7. 7.Use (a + b)(a − b) = a² − b² to find 77 × 63.
8. 8.Use (a − b)² = a² − 2ab + b² to find 39².
9. 9.Use (a − b)² = a² − 2ab + b² to find 63².
10. 10.Use (a + b)² = a² + 2ab + b² to find 83².
11. 11.Use (a − b)² = a² − 2ab + b² to find 77².
12. 12.If a + b = 16 and ab = 55, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 39 × 21.
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 95 × 85.
16. 16.If a + b = 6 and ab = 5, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 11 and y = 4.
18. 18.Use (a + b)² = a² + 2ab + b² to find 36².
19. 19.If a − b = 6 and ab = 40, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 70² − 57².
21. 21.Use (a − b)² = a² − 2ab + b² to find 53².
22. 22.Use (a − b)² = a² − 2ab + b² to find 76².
23. 23.Use (a + b)² = a² + 2ab + b² to find 94².
24. 24.Use (a − b)² = a² − 2ab + b² to find 43².
25. 25.Use a² − b² = (a + b)(a − b) to find 73² − 48².
26. 26.Use (a − b)² = a² − 2ab + b² to find 86².
27. 27.Use (a − b)² = a² − 2ab + b² to find 57².
28. 28.Use a² − b² = (a + b)(a − b) to find 64² − 11².
29. 29.Use a² − b² = (a + b)(a − b) to find 28² − 2².
30. 30.Use (a − b)² = a² − 2ab + b² to find 54².
31. 31.If a + b = 23 and ab = 132, what is a² + b²?
32. 32.If a + b = 10 and ab = 21, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 89².
34. 34.Use (a + b)² = a² + 2ab + b² to find 88².
35. 35.Use (a + b)(a − b) = a² − b² to find 79 × 61.
36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 1.
37. 37.If a + b = 10 and ab = 16, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 48².
39. 39.If a + b = 7 and ab = 6, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 46² − 24².

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