Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 911 · 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 81².
2. 2.Use (a + b)(a − b) = a² − b² to find 55 × 45.
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 104 × 96.
5. 5.Use (a − b)² = a² − 2ab + b² to find 79².
6. 6.Find the value of x² + 2xy + y² when x = 8 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 82 × 78.
8. 8.Use a² − b² = (a + b)(a − b) to find 73² − 5².
9. 9.Use a² − b² = (a + b)(a − b) to find 89² − 6².
10. 10.Use (a + b)(a − b) = a² − b² to find 98 × 82.
11. 11.Use (a + b)(a − b) = a² − b² to find 32 × 28.
12. 12.Use (a + b)(a − b) = a² − b² to find 61 × 59.
13. 13.If a − b = 11 and ab = 12, what is a² + b²?
14. 14.If a − b = 9 and ab = 10, what is a² + b²?
15. 15.Find the value of x² − y² when x = 10 and y = 1.
16. 16.If a − b = 10 and ab = 24, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 57 × 43.
18. 18.Use (a + b)² = a² + 2ab + b² to find 32².
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 7.
20. 20.Use a² − b² = (a + b)(a − b) to find 20² − 5².
21. 21.If a + b = 8 and ab = 15, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 26 × 14.
23. 23.If a + b = 5 and ab = 4, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 71².
25. 25.Use (a + b)² = a² + 2ab + b² to find 31².
26. 26.If a + b = 9 and ab = 20, what is a² + b²?
27. 27.Find the value of x² − y² when x = 5 and y = 1.
28. 28.Find the value of x² − 2xy + y² when x = 6 and y = 2.
29. 29.If a + b = 18 and ab = 77, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 85² − 21².
31. 31.Use (a + b)(a − b) = a² − b² to find 83 × 77.
32. 32.Use (a − b)² = a² − 2ab + b² to find 16².
33. 33.Use (a + b)² = a² + 2ab + b² to find 35².
34. 34.Use a² − b² = (a + b)(a − b) to find 33² − 24².
35. 35.Use a² − b² = (a + b)(a − b) to find 45² − 1².
36. 36.Use (a + b)² = a² + 2ab + b² to find 59².
37. 37.Use a² − b² = (a + b)(a − b) to find 92² − 16².
38. 38.Find the value of x² − 2xy + y² when x = 12 and y = 5.
39. 39.Use (a + b)(a − b) = a² − b² to find 37 × 23.
40. 40.Use (a + b)(a − b) = a² − b² to find 49 × 31.

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