Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 708 · 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 31².
2. 2.If a − b = 1 and ab = 12, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 9 and y = 1.
4. 4.Find the value of x² − y² when x = 15 and y = 1.
5. 5.Find the value of x² − y² when x = 5 and y = 1.
6. 6.Find the value of x² − 2xy + y² when x = 4 and y = 1.
7. 7.Use (a − b)² = a² − 2ab + b² to find 37².
8. 8.Use (a − b)² = a² − 2ab + b² to find 58².
9. 9.Use (a + b)(a − b) = a² − b² to find 55 × 45.
10. 10.Use (a + b)² = a² + 2ab + b² to find 102².
11. 11.If a + b = 22 and ab = 120, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 43² − 38².
13. 13.If a + b = 6 and ab = 5, what is a² + b²?
14. 14.If a + b = 4 and ab = 3, what is a² + b²?
15. 15.If a + b = 5 and ab = 4, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 57².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 3.
18. 18.Use a² − b² = (a + b)(a − b) to find 89² − 8².
19. 19.If a − b = 4 and ab = 32, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 68².
21. 21.Find the value of x² − y² when x = 6 and y = 5.
22. 22.Use (a + b)² = a² + 2ab + b² to find 96².
23. 23.Find the value of x² − 2xy + y² when x = 9 and y = 4.
24. 24.Use (a + b)² = a² + 2ab + b² to find 63².
25. 25.Use (a − b)² = a² − 2ab + b² to find 11².
26. 26.Use a² − b² = (a + b)(a − b) to find 51² − 2².
27. 27.Use (a + b)² = a² + 2ab + b² to find 11².
28. 28.Use a² − b² = (a + b)(a − b) to find 96² − 12².
29. 29.Use (a − b)² = a² − 2ab + b² to find 17².
30. 30.Use a² − b² = (a + b)(a − b) to find 33² − 6².
31. 31.Use (a − b)² = a² − 2ab + b² to find 29².
32. 32.If a − b = 2 and ab = 15, what is a² + b²?
33. 33.Find the value of x² − y² when x = 10 and y = 1.
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 2.
35. 35.If a + b = 8 and ab = 15, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 56².
37. 37.Use (a + b)(a − b) = a² − b² to find 45 × 35.
38. 38.Find the value of x² − y² when x = 13 and y = 11.
39. 39.Use (a − b)² = a² − 2ab + b² to find 31².
40. 40.If a − b = 1 and ab = 6, what is a² + b²?

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