Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 92 · 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 82².
2. 2.Use (a + b)(a − b) = a² − b² to find 91 × 89.
3. 3.Use (a + b)² = a² + 2ab + b² to find 106².
4. 4.Use (a − b)² = a² − 2ab + b² to find 97².
5. 5.If a − b = 1 and ab = 72, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 42² − 18².
7. 7.Use a² − b² = (a + b)(a − b) to find 68² − 21².
8. 8.Use (a − b)² = a² − 2ab + b² to find 19².
9. 9.Find the value of x² + 2xy + y² when x = 11 and y = 2.
10. 10.Use (a + b)² = a² + 2ab + b² to find 55².
11. 11.Use a² − b² = (a + b)(a − b) to find 37² − 34².
12. 12.Use (a − b)² = a² − 2ab + b² to find 55².
13. 13.Use a² − b² = (a + b)(a − b) to find 20² − 4².
14. 14.Use (a − b)² = a² − 2ab + b² to find 99².
15. 15.Use (a − b)² = a² − 2ab + b² to find 39².
16. 16.Use a² − b² = (a + b)(a − b) to find 29² − 18².
17. 17.Use (a − b)² = a² − 2ab + b² to find 96².
18. 18.Use (a + b)(a − b) = a² − b² to find 27 × 13.
19. 19.If a − b = 1 and ab = 6, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 45².
21. 21.Use a² − b² = (a + b)(a − b) to find 38² − 36².
22. 22.Use (a − b)² = a² − 2ab + b² to find 28².
23. 23.If a + b = 5 and ab = 6, what is a² + b²?
24. 24.Find the value of x² + 2xy + y² when x = 7 and y = 4.
25. 25.If a + b = 12 and ab = 32, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 18².
27. 27.Use (a − b)² = a² − 2ab + b² to find 58².
28. 28.Use (a − b)² = a² − 2ab + b² to find 31².
29. 29.Use (a + b)² = a² + 2ab + b² to find 18².
30. 30.Find the value of x² + 2xy + y² when x = 5 and y = 3.
31. 31.Find the value of x² − 2xy + y² when x = 14 and y = 4.
32. 32.Use a² − b² = (a + b)(a − b) to find 96² − 38².
33. 33.Use (a + b)² = a² + 2ab + b² to find 91².
34. 34.Use a² − b² = (a + b)(a − b) to find 85² − 33².
35. 35.Find the value of x² − y² when x = 9 and y = 6.
36. 36.Find the value of x² − y² when x = 10 and y = 4.
37. 37.If a − b = 7 and ab = 18, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 71² − 12².
39. 39.Use (a − b)² = a² − 2ab + b² to find 43².
40. 40.Use a² − b² = (a + b)(a − b) to find 90² − 49².

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