Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 762 · 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 46².
2. 2.Use (a − b)² = a² − 2ab + b² to find 66².
3. 3.Use a² − b² = (a + b)(a − b) to find 77² − 39².
4. 4.If a − b = 2 and ab = 24, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 62² − 5².
6. 6.Use (a − b)² = a² − 2ab + b² to find 28².
7. 7.If a + b = 4 and ab = 3, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 15².
9. 9.Use a² − b² = (a + b)(a − b) to find 63² − 22².
10. 10.Use (a + b)(a − b) = a² − b² to find 49 × 31.
11. 11.Use (a + b)² = a² + 2ab + b² to find 56².
12. 12.Use a² − b² = (a + b)(a − b) to find 76² − 38².
13. 13.If a − b = 2 and ab = 63, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 49².
15. 15.Use (a − b)² = a² − 2ab + b² to find 29².
16. 16.Use (a + b)² = a² + 2ab + b² to find 103².
17. 17.Use (a + b)(a − b) = a² − b² to find 21 × 19.
18. 18.Find the value of x² − 2xy + y² when x = 9 and y = 1.
19. 19.Use (a + b)(a − b) = a² − b² to find 24 × 16.
20. 20.Use (a + b)² = a² + 2ab + b² to find 105².
21. 21.Use (a + b)(a − b) = a² − b² to find 83 × 77.
22. 22.If a + b = 18 and ab = 72, what is a² + b²?
23. 23.Find the value of x² − y² when x = 5 and y = 2.
24. 24.Use (a − b)² = a² − 2ab + b² to find 86².
25. 25.Use (a − b)² = a² − 2ab + b² to find 36².
26. 26.Find the value of x² − y² when x = 13 and y = 7.
27. 27.Use (a + b)(a − b) = a² − b² to find 51 × 49.
28. 28.Use (a − b)² = a² − 2ab + b² to find 16².
29. 29.Use (a − b)² = a² − 2ab + b² to find 47².
30. 30.Use (a − b)² = a² − 2ab + b² to find 78².
31. 31.Use (a + b)(a − b) = a² − b² to find 88 × 72.
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.Use a² − b² = (a + b)(a − b) to find 66² − 17².
34. 34.Find the value of x² − y² when x = 14 and y = 3.
35. 35.Find the value of x² − 2xy + y² when x = 3 and y = 1.
36. 36.Use (a + b)(a − b) = a² − b² to find 48 × 32.
37. 37.If a + b = 17 and ab = 66, what is a² + b²?
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 2.
39. 39.If a − b = 2 and ab = 80, what is a² + b²?
40. 40.If a − b = 3 and ab = 88, what is a² + b²?

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