Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 1 · 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 = 5 and ab = 4, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 6 and y = 5.
3. 3.Use a² − b² = (a + b)(a − b) to find 93² − 63².
4. 4.Use (a + b)² = a² + 2ab + b² to find 52².
5. 5.Use (a − b)² = a² − 2ab + b² to find 24².
6. 6.Use (a − b)² = a² − 2ab + b² to find 41².
7. 7.If a + b = 10 and ab = 21, what is a² + b²?
8. 8.Find the value of x² − y² when x = 12 and y = 9.
9. 9.Use (a − b)² = a² − 2ab + b² to find 57².
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 63².
12. 12.Use a² − b² = (a + b)(a − b) to find 45² − 35².
13. 13.Use a² − b² = (a + b)(a − b) to find 82² − 53².
14. 14.If a + b = 15 and ab = 44, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 83².
16. 16.Use (a + b)² = a² + 2ab + b² to find 27².
17. 17.If a + b = 14 and ab = 33, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 73 × 67.
19. 19.Use a² − b² = (a + b)(a − b) to find 28² − 5².
20. 20.Use (a − b)² = a² − 2ab + b² to find 73².
21. 21.Use (a + b)(a − b) = a² − b² to find 36 × 24.
22. 22.Use (a + b)(a − b) = a² − b² to find 22 × 18.
23. 23.Use (a + b)² = a² + 2ab + b² to find 34².
24. 24.Use a² − b² = (a + b)(a − b) to find 41² − 16².
25. 25.Use (a − b)² = a² − 2ab + b² to find 62².
26. 26.Find the value of x² − y² when x = 6 and y = 5.
27. 27.Use (a + b)² = a² + 2ab + b² to find 49².
28. 28.If a + b = 13 and ab = 12, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 31 × 29.
30. 30.Use (a − b)² = a² − 2ab + b² to find 78².
31. 31.Use (a + b)(a − b) = a² − b² to find 39 × 21.
32. 32.Use a² − b² = (a + b)(a − b) to find 51² − 46².
33. 33.Use (a + b)(a − b) = a² − b² to find 27 × 13.
34. 34.Use (a + b)² = a² + 2ab + b² to find 43².
35. 35.Use a² − b² = (a + b)(a − b) to find 31² − 18².
36. 36.Use (a + b)² = a² + 2ab + b² to find 67².
37. 37.Use a² − b² = (a + b)(a − b) to find 25² − 21².
38. 38.Use (a − b)² = a² − 2ab + b² to find 13².
39. 39.Use (a + b)(a − b) = a² − b² to find 94 × 86.
40. 40.Use (a + b)² = a² + 2ab + b² to find 82².

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