Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 917 · 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 23².
2. 2.If a + b = 5 and ab = 4, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 27² − 10².
4. 4.If a − b = 3 and ab = 10, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 65².
6. 6.Use (a + b)² = a² + 2ab + b² to find 84².
7. 7.If a + b = 13 and ab = 40, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 103².
9. 9.Use (a − b)² = a² − 2ab + b² to find 16².
10. 10.Use (a + b)² = a² + 2ab + b² to find 34².
11. 11.Use (a − b)² = a² − 2ab + b² to find 43².
12. 12.If a − b = 1 and ab = 6, what is a² + b²?
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 32 × 28.
15. 15.Use (a − b)² = a² − 2ab + b² to find 35².
16. 16.Use a² − b² = (a + b)(a − b) to find 30² − 19².
17. 17.Use (a + b)² = a² + 2ab + b² to find 56².
18. 18.Use (a + b)(a − b) = a² − b² to find 97 × 83.
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 29² − 2².
21. 21.Use (a − b)² = a² − 2ab + b² to find 69².
22. 22.If a + b = 10 and ab = 9, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 46² − 8².
24. 24.Find the value of x² + 2xy + y² when x = 3 and y = 1.
25. 25.If a + b = 6 and ab = 8, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 56².
27. 27.If a + b = 4 and ab = 3, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 31² − 2².
29. 29.Use a² − b² = (a + b)(a − b) to find 40² − 23².
30. 30.Use (a + b)(a − b) = a² − b² to find 64 × 56.
31. 31.Use (a + b)² = a² + 2ab + b² to find 36².
32. 32.Use (a + b)² = a² + 2ab + b² to find 73².
33. 33.If a + b = 17 and ab = 72, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 46².
35. 35.Use a² − b² = (a + b)(a − b) to find 44² − 34².
36. 36.Find the value of x² + 2xy + y² when x = 6 and y = 2.
37. 37.Find the value of x² − 2xy + y² when x = 14 and y = 9.
38. 38.Use a² − b² = (a + b)(a − b) to find 82² − 10².
39. 39.If a + b = 12 and ab = 20, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 82².

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