Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 442 · 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 a² − b² = (a + b)(a − b) to find 85² − 66².
2. 2.Use a² − b² = (a + b)(a − b) to find 76² − 21².
3. 3.Use (a − b)² = a² − 2ab + b² to find 43².
4. 4.Use a² − b² = (a + b)(a − b) to find 31² − 7².
5. 5.Use (a + b)(a − b) = a² − b² to find 104 × 96.
6. 6.Use a² − b² = (a + b)(a − b) to find 95² − 49².
7. 7.Use (a − b)² = a² − 2ab + b² to find 19².
8. 8.If a + b = 16 and ab = 48, what is a² + b²?
9. 9.Find the value of x² − y² when x = 12 and y = 7.
10. 10.Use (a + b)² = a² + 2ab + b² to find 24².
11. 11.Use (a + b)² = a² + 2ab + b² to find 43².
12. 12.Use (a + b)² = a² + 2ab + b² to find 92².
13. 13.Use a² − b² = (a + b)(a − b) to find 35² − 8².
14. 14.Use (a − b)² = a² − 2ab + b² to find 76².
15. 15.Use (a + b)(a − b) = a² − b² to find 107 × 93.
16. 16.Use (a + b)(a − b) = a² − b² to find 68 × 52.
17. 17.If a − b = 1 and ab = 2, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 62².
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 10.
20. 20.Use (a + b)(a − b) = a² − b² to find 75 × 65.
21. 21.Use (a + b)² = a² + 2ab + b² to find 83².
22. 22.Use a² − b² = (a + b)(a − b) to find 81² − 13².
23. 23.Use (a + b)(a − b) = a² − b² to find 82 × 78.
24. 24.Use a² − b² = (a + b)(a − b) to find 95² − 39².
25. 25.Use (a + b)² = a² + 2ab + b² to find 38².
26. 26.Use (a + b)² = a² + 2ab + b² to find 36².
27. 27.Use (a + b)(a − b) = a² − b² to find 26 × 14.
28. 28.Find the value of x² − 2xy + y² when x = 6 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 68².
30. 30.Use a² − b² = (a + b)(a − b) to find 30² − 16².
31. 31.Find the value of x² + 2xy + y² when x = 8 and y = 5.
32. 32.If a + b = 5 and ab = 6, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 6 and y = 4.
34. 34.Use (a + b)(a − b) = a² − b² to find 24 × 16.
35. 35.Find the value of x² + 2xy + y² when x = 12 and y = 8.
36. 36.Find the value of x² + 2xy + y² when x = 3 and y = 1.
37. 37.Find the value of x² + 2xy + y² when x = 8 and y = 4.
38. 38.Find the value of x² + 2xy + y² when x = 9 and y = 4.
39. 39.Use (a − b)² = a² − 2ab + b² to find 22².
40. 40.If a + b = 8 and ab = 15, what is a² + b²?

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