Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 136 · 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 = 1 and ab = 2, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 18².
3. 3.Use (a + b)² = a² + 2ab + b² to find 82².
4. 4.Use (a − b)² = a² − 2ab + b² to find 86².
5. 5.Use (a + b)² = a² + 2ab + b² to find 11².
6. 6.Use (a + b)² = a² + 2ab + b² to find 31².
7. 7.Find the value of x² + 2xy + y² when x = 5 and y = 1.
8. 8.Use (a − b)² = a² − 2ab + b² to find 71².
9. 9.Use a² − b² = (a + b)(a − b) to find 35² − 12².
10. 10.Use (a + b)(a − b) = a² − b² to find 102 × 98.
11. 11.Use (a + b)(a − b) = a² − b² to find 52 × 48.
12. 12.Use (a − b)² = a² − 2ab + b² to find 19².
13. 13.Use (a − b)² = a² − 2ab + b² to find 11².
14. 14.Use (a + b)² = a² + 2ab + b² to find 33².
15. 15.If a − b = 8 and ab = 20, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 42² − 13².
17. 17.If a + b = 11 and ab = 10, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 36² − 30².
19. 19.Use a² − b² = (a + b)(a − b) to find 81² − 15².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.Use (a + b)(a − b) = a² − b² to find 66 × 54.
22. 22.Use (a + b)(a − b) = a² − b² to find 81 × 79.
23. 23.If a + b = 4 and ab = 3, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 59².
25. 25.Use a² − b² = (a + b)(a − b) to find 51² − 50².
26. 26.Use (a + b)² = a² + 2ab + b² to find 23².
27. 27.Find the value of x² + 2xy + y² when x = 12 and y = 3.
28. 28.If a − b = 2 and ab = 3, what is a² + b²?
29. 29.If a + b = 15 and ab = 50, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 46².
31. 31.Use a² − b² = (a + b)(a − b) to find 66² − 37².
32. 32.Use (a + b)² = a² + 2ab + b² to find 74².
33. 33.Use (a + b)(a − b) = a² − b² to find 63 × 57.
34. 34.Use (a + b)² = a² + 2ab + b² to find 99².
35. 35.Use a² − b² = (a + b)(a − b) to find 57² − 16².
36. 36.Use (a + b)² = a² + 2ab + b² to find 93².
37. 37.Use (a − b)² = a² − 2ab + b² to find 64².
38. 38.Find the value of x² + 2xy + y² when x = 15 and y = 13.
39. 39.Use (a + b)(a − b) = a² − b² to find 36 × 24.
40. 40.Use a² − b² = (a + b)(a − b) to find 80² − 79².

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