Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 868 · 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 99² − 21².
2. 2.Use (a − b)² = a² − 2ab + b² to find 22².
3. 3.Use (a − b)² = a² − 2ab + b² to find 59².
4. 4.Use a² − b² = (a + b)(a − b) to find 49² − 25².
5. 5.Use (a + b)² = a² + 2ab + b² to find 86².
6. 6.Use (a − b)² = a² − 2ab + b² to find 31².
7. 7.Use a² − b² = (a + b)(a − b) to find 40² − 5².
8. 8.If a + b = 6 and ab = 8, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 48 × 32.
10. 10.Use (a + b)² = a² + 2ab + b² to find 23².
11. 11.Use (a + b)(a − b) = a² − b² to find 34 × 26.
12. 12.Use (a + b)(a − b) = a² − b² to find 98 × 82.
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 2.
14. 14.Use (a − b)² = a² − 2ab + b² to find 86².
15. 15.Use (a − b)² = a² − 2ab + b² to find 27².
16. 16.Use (a + b)² = a² + 2ab + b² to find 71².
17. 17.If a + b = 13 and ab = 42, what is a² + b²?
18. 18.If a + b = 12 and ab = 11, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 71² − 21².
20. 20.Use (a + b)² = a² + 2ab + b² to find 107².
21. 21.Use (a + b)² = a² + 2ab + b² to find 49².
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.If a + b = 19 and ab = 90, what is a² + b²?
24. 24.If a + b = 7 and ab = 10, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 14 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 54².
27. 27.Use (a + b)(a − b) = a² − b² to find 32 × 28.
28. 28.If a + b = 8 and ab = 7, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 28².
30. 30.Use (a + b)² = a² + 2ab + b² to find 68².
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.If a + b = 5 and ab = 4, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 63 × 57.
34. 34.Use (a − b)² = a² − 2ab + b² to find 34².
35. 35.Use (a − b)² = a² − 2ab + b² to find 93².
36. 36.Use a² − b² = (a + b)(a − b) to find 33² − 31².
37. 37.Find the value of x² − 2xy + y² when x = 3 and y = 2.
38. 38.Use a² − b² = (a + b)(a − b) to find 56² − 2².
39. 39.Use (a − b)² = a² − 2ab + b² to find 29².
40. 40.Use (a − b)² = a² − 2ab + b² to find 18².

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