Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 794 · 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.If a − b = 4 and ab = 5, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 78 × 62.
3. 3.Find the value of x² − 2xy + y² when x = 5 and y = 4.
4. 4.Find the value of x² + 2xy + y² when x = 9 and y = 3.
5. 5.Use a² − b² = (a + b)(a − b) to find 43² − 11².
6. 6.Use (a − b)² = a² − 2ab + b² to find 52².
7. 7.Use (a + b)(a − b) = a² − b² to find 47 × 33.
8. 8.Use (a − b)² = a² − 2ab + b² to find 21².
9. 9.If a + b = 21 and ab = 110, what is a² + b²?
10. 10.If a − b = 5 and ab = 6, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 67² − 52².
12. 12.Use (a + b)² = a² + 2ab + b² to find 95².
13. 13.Use (a − b)² = a² − 2ab + b² to find 62².
14. 14.Use (a + b)(a − b) = a² − b² to find 67 × 53.
15. 15.Find the value of x² − 2xy + y² when x = 5 and y = 3.
16. 16.Use (a − b)² = a² − 2ab + b² to find 35².
17. 17.Use (a − b)² = a² − 2ab + b² to find 31².
18. 18.Use (a + b)² = a² + 2ab + b² to find 49².
19. 19.Use (a + b)² = a² + 2ab + b² to find 37².
20. 20.If a − b = 7 and ab = 18, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 57² − 23².
22. 22.Use (a + b)² = a² + 2ab + b² to find 35².
23. 23.Find the value of x² − y² when x = 11 and y = 3.
24. 24.Use (a + b)(a − b) = a² − b² to find 101 × 99.
25. 25.Use (a − b)² = a² − 2ab + b² to find 69².
26. 26.Use a² − b² = (a + b)(a − b) to find 63² − 50².
27. 27.If a + b = 10 and ab = 9, what is a² + b²?
28. 28.Find the value of x² − 2xy + y² when x = 8 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 36² − 23².
30. 30.Use a² − b² = (a + b)(a − b) to find 49² − 8².
31. 31.Find the value of x² − y² when x = 6 and y = 4.
32. 32.Use a² − b² = (a + b)(a − b) to find 32² − 2².
33. 33.Use a² − b² = (a + b)(a − b) to find 76² − 5².
34. 34.Use a² − b² = (a + b)(a − b) to find 95² − 26².
35. 35.If a + b = 12 and ab = 11, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 83².
37. 37.Use (a + b)(a − b) = a² − b² to find 62 × 58.
38. 38.Use (a + b)² = a² + 2ab + b² to find 52².
39. 39.Find the value of x² − y² when x = 7 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 23².

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