Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 266 · 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 95².
2. 2.Use (a − b)² = a² − 2ab + b² to find 73².
3. 3.Use (a + b)² = a² + 2ab + b² to find 45².
4. 4.If a − b = 3 and ab = 88, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 21².
6. 6.Use (a − b)² = a² − 2ab + b² to find 16².
7. 7.Use a² − b² = (a + b)(a − b) to find 46² − 36².
8. 8.Use (a + b)² = a² + 2ab + b² to find 98².
9. 9.Use (a + b)² = a² + 2ab + b² to find 11².
10. 10.Use a² − b² = (a + b)(a − b) to find 30² − 9².
11. 11.Use (a + b)(a − b) = a² − b² to find 87 × 73.
12. 12.If a + b = 12 and ab = 20, what is a² + b²?
13. 13.If a + b = 17 and ab = 60, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 106 × 94.
15. 15.Use (a − b)² = a² − 2ab + b² to find 38².
16. 16.Use (a + b)² = a² + 2ab + b² to find 38².
17. 17.Use (a + b)² = a² + 2ab + b² to find 25².
18. 18.Use a² − b² = (a + b)(a − b) to find 22² − 16².
19. 19.Use (a − b)² = a² − 2ab + b² to find 25².
20. 20.Use (a + b)(a − b) = a² − b² to find 75 × 65.
21. 21.Use (a + b)² = a² + 2ab + b² to find 15².
22. 22.Use (a + b)(a − b) = a² − b² to find 89 × 71.
23. 23.Use a² − b² = (a + b)(a − b) to find 77² − 34².
24. 24.If a + b = 4 and ab = 3, what is a² + b²?
25. 25.Find the value of x² − y² when x = 3 and y = 2.
26. 26.Use (a + b)² = a² + 2ab + b² to find 78².
27. 27.Use (a + b)(a − b) = a² − b² to find 46 × 34.
28. 28.Use a² − b² = (a + b)(a − b) to find 23² − 8².
29. 29.Use (a − b)² = a² − 2ab + b² to find 98².
30. 30.Use (a − b)² = a² − 2ab + b² to find 24².
31. 31.If a − b = 3 and ab = 4, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 76² − 35².
33. 33.If a + b = 10 and ab = 9, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 7 and y = 5.
35. 35.Use (a + b)² = a² + 2ab + b² to find 107².
36. 36.Use (a + b)(a − b) = a² − b² to find 58 × 42.
37. 37.If a − b = 5 and ab = 66, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Use (a − b)² = a² − 2ab + b² to find 15².
40. 40.If a − b = 1 and ab = 2, what is a² + b²?

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