Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 423 · 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 13².
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 39².
4. 4.Use a² − b² = (a + b)(a − b) to find 78² − 52².
5. 5.Use (a + b)² = a² + 2ab + b² to find 26².
6. 6.Find the value of x² + 2xy + y² when x = 7 and y = 4.
7. 7.If a + b = 18 and ab = 80, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 36 × 24.
9. 9.Find the value of x² + 2xy + y² when x = 10 and y = 9.
10. 10.If a + b = 8 and ab = 12, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 45² − 2².
12. 12.Use (a + b)² = a² + 2ab + b² to find 92².
13. 13.Use a² − b² = (a + b)(a − b) to find 28² − 14².
14. 14.Use (a − b)² = a² − 2ab + b² to find 31².
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 49².
17. 17.Use (a + b)² = a² + 2ab + b² to find 103².
18. 18.Use a² − b² = (a + b)(a − b) to find 57² − 46².
19. 19.If a − b = 1 and ab = 132, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 105².
21. 21.Use (a + b)² = a² + 2ab + b² to find 58².
22. 22.Find the value of x² − y² when x = 14 and y = 7.
23. 23.Use a² − b² = (a + b)(a − b) to find 43² − 3².
24. 24.Use a² − b² = (a + b)(a − b) to find 64² − 42².
25. 25.Use (a + b)² = a² + 2ab + b² to find 49².
26. 26.Use (a + b)² = a² + 2ab + b² to find 11².
27. 27.If a − b = 1 and ab = 6, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 13².
29. 29.Find the value of x² − y² when x = 15 and y = 4.
30. 30.Use (a + b)² = a² + 2ab + b² to find 32².
31. 31.Use (a − b)² = a² − 2ab + b² to find 77².
32. 32.Use (a + b)² = a² + 2ab + b² to find 24².
33. 33.Use (a − b)² = a² − 2ab + b² to find 16².
34. 34.If a − b = 6 and ab = 27, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 5.
36. 36.Use a² − b² = (a + b)(a − b) to find 28² − 23².
37. 37.Use (a − b)² = a² − 2ab + b² to find 76².
38. 38.If a + b = 14 and ab = 48, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 48².
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 1.

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