Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 395 · 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 22².
2. 2.Use (a + b)² = a² + 2ab + b² to find 51².
3. 3.Use (a + b)² = a² + 2ab + b² to find 44².
4. 4.Use (a + b)² = a² + 2ab + b² to find 93².
5. 5.Use (a + b)(a − b) = a² − b² to find 91 × 89.
6. 6.Use a² − b² = (a + b)(a − b) to find 64² − 29².
7. 7.Use (a + b)² = a² + 2ab + b² to find 55².
8. 8.If a + b = 13 and ab = 40, what is a² + b²?
9. 9.Find the value of x² − 2xy + y² when x = 13 and y = 9.
10. 10.Use (a + b)² = a² + 2ab + b² to find 14².
11. 11.Use a² − b² = (a + b)(a − b) to find 73² − 10².
12. 12.Use a² − b² = (a + b)(a − b) to find 45² − 23².
13. 13.If a + b = 9 and ab = 14, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 39² − 27².
15. 15.Use a² − b² = (a + b)(a − b) to find 21² − 5².
16. 16.Find the value of x² − 2xy + y² when x = 7 and y = 3.
17. 17.Use (a + b)² = a² + 2ab + b² to find 83².
18. 18.Find the value of x² − 2xy + y² when x = 9 and y = 6.
19. 19.Use (a + b)² = a² + 2ab + b² to find 106².
20. 20.Find the value of x² − y² when x = 13 and y = 5.
21. 21.Use a² − b² = (a + b)(a − b) to find 77² − 2².
22. 22.Use (a + b)² = a² + 2ab + b² to find 86².
23. 23.Use (a + b)(a − b) = a² − b² to find 109 × 91.
24. 24.If a − b = 2 and ab = 24, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 108².
26. 26.If a + b = 13 and ab = 30, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 54².
28. 28.Use a² − b² = (a + b)(a − b) to find 63² − 58².
29. 29.If a − b = 2 and ab = 99, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 54 × 46.
31. 31.Use (a + b)² = a² + 2ab + b² to find 72².
32. 32.Use a² − b² = (a + b)(a − b) to find 42² − 24².
33. 33.Use (a + b)(a − b) = a² − b² to find 76 × 64.
34. 34.Use (a − b)² = a² − 2ab + b² to find 53².
35. 35.Use (a − b)² = a² − 2ab + b² to find 46².
36. 36.Use (a + b)(a − b) = a² − b² to find 36 × 24.
37. 37.Use (a − b)² = a² − 2ab + b² to find 95².
38. 38.If a + b = 12 and ab = 20, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 31².
40. 40.Use (a − b)² = a² − 2ab + b² to find 33².

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