Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 90 · 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 17².
2. 2.Use (a + b)² = a² + 2ab + b² to find 53².
3. 3.Find the value of x² − 2xy + y² when x = 7 and y = 1.
4. 4.If a − b = 2 and ab = 8, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 105 × 95.
6. 6.If a + b = 18 and ab = 80, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 42² − 12².
8. 8.Use (a − b)² = a² − 2ab + b² to find 12².
9. 9.Use (a − b)² = a² − 2ab + b² to find 19².
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 1.
11. 11.Use a² − b² = (a + b)(a − b) to find 31² − 7².
12. 12.If a − b = 1 and ab = 56, what is a² + b²?
13. 13.If a − b = 1 and ab = 2, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 99² − 62².
15. 15.If a − b = 2 and ab = 3, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 78 × 62.
17. 17.Find the value of x² − y² when x = 8 and y = 5.
18. 18.If a + b = 10 and ab = 9, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 66 × 54.
20. 20.If a − b = 3 and ab = 28, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 15².
22. 22.Use (a − b)² = a² − 2ab + b² to find 71².
23. 23.Find the value of x² + 2xy + y² when x = 14 and y = 10.
24. 24.Find the value of x² − y² when x = 14 and y = 13.
25. 25.Use a² − b² = (a + b)(a − b) to find 82² − 5².
26. 26.Find the value of x² + 2xy + y² when x = 12 and y = 5.
27. 27.Use (a − b)² = a² − 2ab + b² to find 66².
28. 28.Find the value of x² + 2xy + y² when x = 4 and y = 3.
29. 29.Use (a + b)² = a² + 2ab + b² to find 42².
30. 30.If a + b = 6 and ab = 8, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 62² − 8².
32. 32.Use a² − b² = (a + b)(a − b) to find 85² − 10².
33. 33.Use (a + b)(a − b) = a² − b² to find 46 × 34.
34. 34.If a − b = 1 and ab = 12, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 14 and y = 7.
36. 36.Use (a − b)² = a² − 2ab + b² to find 72².
37. 37.Use (a − b)² = a² − 2ab + b² to find 46².
38. 38.Use (a + b)² = a² + 2ab + b² to find 21².
39. 39.Use (a + b)(a − b) = a² − b² to find 37 × 23.
40. 40.Use (a + b)(a − b) = a² − b² to find 77 × 63.

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