Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 18 · 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 = 13 and ab = 36, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 87².
3. 3.Use (a + b)² = a² + 2ab + b² to find 86².
4. 4.Use (a + b)² = a² + 2ab + b² to find 95².
5. 5.Use (a + b)(a − b) = a² − b² to find 62 × 58.
6. 6.Use (a + b)(a − b) = a² − b² to find 26 × 14.
7. 7.If a + b = 10 and ab = 9, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 75².
9. 9.Use (a − b)² = a² − 2ab + b² to find 37².
10. 10.Use a² − b² = (a + b)(a − b) to find 99² − 93².
11. 11.Use (a − b)² = a² − 2ab + b² to find 16².
12. 12.Use (a + b)(a − b) = a² − b² to find 25 × 15.
13. 13.Find the value of x² + 2xy + y² when x = 7 and y = 3.
14. 14.Use (a + b)(a − b) = a² − b² to find 42 × 38.
15. 15.Use (a + b)(a − b) = a² − b² to find 73 × 67.
16. 16.Use a² − b² = (a + b)(a − b) to find 53² − 46².
17. 17.Use (a + b)² = a² + 2ab + b² to find 65².
18. 18.Use (a − b)² = a² − 2ab + b² to find 18².
19. 19.Use (a − b)² = a² − 2ab + b² to find 63².
20. 20.Find the value of x² + 2xy + y² when x = 6 and y = 5.
21. 21.Use a² − b² = (a + b)(a − b) to find 44² − 34².
22. 22.Use (a + b)² = a² + 2ab + b² to find 22².
23. 23.Find the value of x² − 2xy + y² when x = 8 and y = 4.
24. 24.If a − b = 1 and ab = 6, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 17².
26. 26.Use (a + b)(a − b) = a² − b² to find 81 × 79.
27. 27.Use (a + b)² = a² + 2ab + b² to find 87².
28. 28.Use (a + b)(a − b) = a² − b² to find 103 × 97.
29. 29.Use (a + b)(a − b) = a² − b² to find 51 × 49.
30. 30.Find the value of x² − 2xy + y² when x = 10 and y = 7.
31. 31.Find the value of x² − y² when x = 10 and y = 9.
32. 32.Use a² − b² = (a + b)(a − b) to find 96² − 1².
33. 33.Use (a + b)² = a² + 2ab + b² to find 59².
34. 34.Use a² − b² = (a + b)(a − b) to find 56² − 19².
35. 35.Use a² − b² = (a + b)(a − b) to find 68² − 43².
36. 36.Use a² − b² = (a + b)(a − b) to find 41² − 36².
37. 37.Use (a − b)² = a² − 2ab + b² to find 66².
38. 38.Find the value of x² + 2xy + y² when x = 13 and y = 3.
39. 39.Find the value of x² − 2xy + y² when x = 12 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 49² − 18².

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