Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 333 · 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.Find the value of x² + 2xy + y² when x = 8 and y = 1.
2. 2.Use (a + b)² = a² + 2ab + b² to find 33².
3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 3.
4. 4.Use a² − b² = (a + b)(a − b) to find 36² − 31².
5. 5.Use (a + b)(a − b) = a² − b² to find 24 × 16.
6. 6.Use a² − b² = (a + b)(a − b) to find 89² − 76².
7. 7.Use a² − b² = (a + b)(a − b) to find 26² − 20².
8. 8.Use a² − b² = (a + b)(a − b) to find 91² − 81².
9. 9.Use a² − b² = (a + b)(a − b) to find 80² − 28².
10. 10.Use (a + b)² = a² + 2ab + b² to find 78².
11. 11.Use a² − b² = (a + b)(a − b) to find 36² − 33².
12. 12.If a + b = 8 and ab = 7, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 31² − 28².
14. 14.Use (a − b)² = a² − 2ab + b² to find 12².
15. 15.If a + b = 8 and ab = 12, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 12².
17. 17.Find the value of x² − y² when x = 5 and y = 3.
18. 18.Find the value of x² − 2xy + y² when x = 14 and y = 9.
19. 19.Use (a + b)² = a² + 2ab + b² to find 74².
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Use (a − b)² = a² − 2ab + b² to find 33².
22. 22.If a − b = 4 and ab = 5, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 54².
24. 24.If a + b = 13 and ab = 42, what is a² + b²?
25. 25.If a − b = 4 and ab = 12, what is a² + b²?
26. 26.If a − b = 2 and ab = 99, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 83² − 65².
28. 28.If a + b = 15 and ab = 50, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 93² − 10².
30. 30.Use (a − b)² = a² − 2ab + b² to find 69².
31. 31.Find the value of x² + 2xy + y² when x = 10 and y = 8.
32. 32.Use (a − b)² = a² − 2ab + b² to find 55².
33. 33.Use (a + b)² = a² + 2ab + b² to find 14².
34. 34.Use (a + b)² = a² + 2ab + b² to find 79².
35. 35.Find the value of x² − 2xy + y² when x = 5 and y = 1.
36. 36.Use (a + b)² = a² + 2ab + b² to find 35².
37. 37.Find the value of x² − 2xy + y² when x = 9 and y = 6.
38. 38.Use a² − b² = (a + b)(a − b) to find 72² − 63².
39. 39.Use (a − b)² = a² − 2ab + b² to find 27².
40. 40.Use a² − b² = (a + b)(a − b) to find 33² − 8².

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