Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 98 · 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 16².
2. 2.Find the value of x² + 2xy + y² when x = 13 and y = 8.
3. 3.Use (a − b)² = a² − 2ab + b² to find 17².
4. 4.Use (a + b)(a − b) = a² − b² to find 43 × 37.
5. 5.Use (a + b)(a − b) = a² − b² to find 21 × 19.
6. 6.Use a² − b² = (a + b)(a − b) to find 68² − 27².
7. 7.Use a² − b² = (a + b)(a − b) to find 55² − 54².
8. 8.Use a² − b² = (a + b)(a − b) to find 43² − 35².
9. 9.Use (a + b)² = a² + 2ab + b² to find 79².
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 1.
11. 11.Use (a + b)(a − b) = a² − b² to find 48 × 32.
12. 12.Use (a + b)² = a² + 2ab + b² to find 29².
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.If a + b = 14 and ab = 33, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 83² − 27².
16. 16.Use (a − b)² = a² − 2ab + b² to find 75².
17. 17.Use (a + b)(a − b) = a² − b² to find 98 × 82.
18. 18.Use (a + b)² = a² + 2ab + b² to find 31².
19. 19.Use (a + b)² = a² + 2ab + b² to find 11².
20. 20.Use (a + b)² = a² + 2ab + b² to find 71².
21. 21.Use (a − b)² = a² − 2ab + b² to find 31².
22. 22.Use (a − b)² = a² − 2ab + b² to find 51².
23. 23.If a − b = 8 and ab = 9, what is a² + b²?
24. 24.Find the value of x² − y² when x = 4 and y = 1.
25. 25.Find the value of x² − y² when x = 8 and y = 4.
26. 26.If a + b = 7 and ab = 10, what is a² + b²?
27. 27.Find the value of x² − y² when x = 14 and y = 7.
28. 28.If a − b = 1 and ab = 2, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 19².
30. 30.Use (a − b)² = a² − 2ab + b² to find 29².
31. 31.Find the value of x² + 2xy + y² when x = 10 and y = 9.
32. 32.Use a² − b² = (a + b)(a − b) to find 58² − 4².
33. 33.Use (a − b)² = a² − 2ab + b² to find 96².
34. 34.If a − b = 8 and ab = 33, what is a² + b²?
35. 35.If a + b = 9 and ab = 20, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 61².
37. 37.Find the value of x² − 2xy + y² when x = 9 and y = 2.
38. 38.If a − b = 2 and ab = 8, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 84².
40. 40.If a + b = 3 and ab = 2, what is a² + b²?

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