Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 747 · 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 69².
2. 2.Use (a − b)² = a² − 2ab + b² to find 82².
3. 3.If a − b = 3 and ab = 18, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 22 × 18.
5. 5.Use (a + b)² = a² + 2ab + b² to find 47².
6. 6.If a − b = 4 and ab = 60, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 12 and y = 4.
8. 8.Use (a + b)(a − b) = a² − b² to find 47 × 33.
9. 9.If a + b = 10 and ab = 21, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 31².
11. 11.Use a² − b² = (a + b)(a − b) to find 34² − 13².
12. 12.Find the value of x² − 2xy + y² when x = 13 and y = 4.
13. 13.Use (a + b)² = a² + 2ab + b² to find 19².
14. 14.Use (a + b)² = a² + 2ab + b² to find 23².
15. 15.Use (a + b)(a − b) = a² − b² to find 55 × 45.
16. 16.Find the value of x² + 2xy + y² when x = 15 and y = 11.
17. 17.Use (a + b)(a − b) = a² − b² to find 61 × 59.
18. 18.If a + b = 9 and ab = 8, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 99² − 37².
21. 21.If a − b = 2 and ab = 3, what is a² + b²?
22. 22.If a − b = 5 and ab = 14, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 24².
24. 24.Find the value of x² − y² when x = 4 and y = 2.
25. 25.Find the value of x² − y² when x = 14 and y = 4.
26. 26.Use a² − b² = (a + b)(a − b) to find 54² − 23².
27. 27.Use (a + b)² = a² + 2ab + b² to find 11².
28. 28.If a − b = 1 and ab = 2, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 29².
30. 30.Find the value of x² − 2xy + y² when x = 5 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 59².
32. 32.Find the value of x² − 2xy + y² when x = 11 and y = 3.
33. 33.Use a² − b² = (a + b)(a − b) to find 85² − 56².
34. 34.Use (a − b)² = a² − 2ab + b² to find 52².
35. 35.Use a² − b² = (a + b)(a − b) to find 83² − 75².
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.If a − b = 3 and ab = 54, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 78².
39. 39.Use (a + b)² = a² + 2ab + b² to find 43².
40. 40.Use (a − b)² = a² − 2ab + b² to find 69².

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