Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 786 · 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 53².
2. 2.Use (a + b)(a − b) = a² − b² to find 22 × 18.
3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
4. 4.If a − b = 2 and ab = 63, what is a² + b²?
5. 5.If a + b = 11 and ab = 28, what is a² + b²?
6. 6.If a − b = 5 and ab = 66, what is a² + b²?
7. 7.Find the value of x² − y² when x = 12 and y = 11.
8. 8.If a − b = 3 and ab = 18, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 55 × 45.
10. 10.If a + b = 17 and ab = 60, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 83².
12. 12.Use a² − b² = (a + b)(a − b) to find 21² − 11².
13. 13.Use (a + b)(a − b) = a² − b² to find 33 × 27.
14. 14.Use (a + b)² = a² + 2ab + b² to find 11².
15. 15.Find the value of x² − y² when x = 4 and y = 2.
16. 16.Use (a − b)² = a² − 2ab + b² to find 75².
17. 17.Use (a + b)² = a² + 2ab + b² to find 37².
18. 18.If a − b = 1 and ab = 12, what is a² + b²?
19. 19.If a − b = 7 and ab = 18, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 35² − 2².
21. 21.If a + b = 5 and ab = 6, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 27² − 5².
23. 23.Find the value of x² − y² when x = 11 and y = 5.
24. 24.Use (a + b)² = a² + 2ab + b² to find 12².
25. 25.Use (a − b)² = a² − 2ab + b² to find 96².
26. 26.Use a² − b² = (a + b)(a − b) to find 89² − 37².
27. 27.Use (a − b)² = a² − 2ab + b² to find 94².
28. 28.Use (a + b)² = a² + 2ab + b² to find 56².
29. 29.Find the value of x² − y² when x = 5 and y = 3.
30. 30.Use (a − b)² = a² − 2ab + b² to find 24².
31. 31.Use (a + b)² = a² + 2ab + b² to find 18².
32. 32.Use (a − b)² = a² − 2ab + b² to find 19².
33. 33.Find the value of x² + 2xy + y² when x = 8 and y = 4.
34. 34.Use (a + b)² = a² + 2ab + b² to find 34².
35. 35.Use (a + b)(a − b) = a² − b² to find 45 × 35.
36. 36.Use a² − b² = (a + b)(a − b) to find 49² − 31².
37. 37.If a − b = 1 and ab = 20, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 26².
39. 39.Use a² − b² = (a + b)(a − b) to find 30² − 10².
40. 40.Use (a + b)(a − b) = a² − b² to find 57 × 43.

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