Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 745 · 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 35².
2. 2.Use (a − b)² = a² − 2ab + b² to find 41².
3. 3.Use (a + b)² = a² + 2ab + b² to find 13².
4. 4.Use (a − b)² = a² − 2ab + b² to find 71².
5. 5.Use (a − b)² = a² − 2ab + b² to find 21².
6. 6.If a − b = 9 and ab = 36, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 17².
8. 8.If a + b = 6 and ab = 8, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 86² − 65².
10. 10.Find the value of x² − y² when x = 10 and y = 8.
11. 11.Use (a + b)² = a² + 2ab + b² to find 103².
12. 12.Find the value of x² + 2xy + y² when x = 8 and y = 6.
13. 13.Find the value of x² + 2xy + y² when x = 13 and y = 9.
14. 14.Use (a + b)(a − b) = a² − b² to find 41 × 39.
15. 15.If a − b = 4 and ab = 21, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 79² − 52².
17. 17.Use (a + b)² = a² + 2ab + b² to find 66².
18. 18.Use (a − b)² = a² − 2ab + b² to find 88².
19. 19.Use (a + b)(a − b) = a² − b² to find 82 × 78.
20. 20.Use (a + b)² = a² + 2ab + b² to find 61².
21. 21.Use (a − b)² = a² − 2ab + b² to find 77².
22. 22.Use (a + b)² = a² + 2ab + b² to find 96².
23. 23.Use a² − b² = (a + b)(a − b) to find 36² − 7².
24. 24.Use (a + b)(a − b) = a² − b² to find 69 × 51.
25. 25.Use (a − b)² = a² − 2ab + b² to find 34².
26. 26.Use a² − b² = (a + b)(a − b) to find 87² − 26².
27. 27.Use (a − b)² = a² − 2ab + b² to find 57².
28. 28.If a − b = 7 and ab = 44, what is a² + b²?
29. 29.Find the value of x² − 2xy + y² when x = 13 and y = 9.
30. 30.Use a² − b² = (a + b)(a − b) to find 72² − 9².
31. 31.Use (a + b)(a − b) = a² − b² to find 26 × 14.
32. 32.Use (a + b)² = a² + 2ab + b² to find 109².
33. 33.Find the value of x² + 2xy + y² when x = 11 and y = 6.
34. 34.If a − b = 4 and ab = 32, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 27².
36. 36.Use (a − b)² = a² − 2ab + b² to find 94².
37. 37.Use (a − b)² = a² − 2ab + b² to find 17².
38. 38.Use (a − b)² = a² − 2ab + b² to find 47².
39. 39.Use a² − b² = (a + b)(a − b) to find 32² − 2².
40. 40.Use (a + b)² = a² + 2ab + b² to find 12².

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