Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 859 · 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.Find the value of x² − 2xy + y² when x = 7 and y = 1.
2. 2.If a + b = 14 and ab = 40, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 56² − 21².
4. 4.Use a² − b² = (a + b)(a − b) to find 61² − 7².
5. 5.If a + b = 14 and ab = 48, what is a² + b²?
6. 6.If a − b = 2 and ab = 3, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 34².
8. 8.Use (a + b)(a − b) = a² − b² to find 64 × 56.
9. 9.Use (a − b)² = a² − 2ab + b² to find 11².
10. 10.If a + b = 9 and ab = 20, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 17².
12. 12.If a + b = 16 and ab = 63, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 12 and y = 8.
14. 14.Use a² − b² = (a + b)(a − b) to find 22² − 3².
15. 15.Use a² − b² = (a + b)(a − b) to find 24² − 13².
16. 16.Use a² − b² = (a + b)(a − b) to find 84² − 18².
17. 17.Use (a + b)(a − b) = a² − b² to find 56 × 44.
18. 18.Use (a − b)² = a² − 2ab + b² to find 74².
19. 19.Use a² − b² = (a + b)(a − b) to find 62² − 27².
20. 20.Use (a − b)² = a² − 2ab + b² to find 71².
21. 21.Find the value of x² + 2xy + y² when x = 3 and y = 2.
22. 22.If a + b = 9 and ab = 18, what is a² + b²?
23. 23.Find the value of x² − y² when x = 13 and y = 8.
24. 24.Use (a − b)² = a² − 2ab + b² to find 89².
25. 25.Find the value of x² + 2xy + y² when x = 15 and y = 5.
26. 26.Use (a + b)(a − b) = a² − b² to find 99 × 81.
27. 27.Use a² − b² = (a + b)(a − b) to find 31² − 6².
28. 28.If a + b = 9 and ab = 8, what is a² + b²?
29. 29.If a − b = 4 and ab = 12, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 16².
31. 31.Find the value of x² + 2xy + y² when x = 4 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 93 × 87.
33. 33.Use (a + b)² = a² + 2ab + b² to find 12².
34. 34.Use (a + b)(a − b) = a² − b² to find 83 × 77.
35. 35.Use a² − b² = (a + b)(a − b) to find 27² − 4².
36. 36.Use a² − b² = (a + b)(a − b) to find 57² − 35².
37. 37.Use (a + b)(a − b) = a² − b² to find 39 × 21.
38. 38.Use (a + b)(a − b) = a² − b² to find 43 × 37.
39. 39.Use a² − b² = (a + b)(a − b) to find 80² − 8².
40. 40.Use (a − b)² = a² − 2ab + b² to find 37².

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