Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 108 · 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 92².
2. 2.Use a² − b² = (a + b)(a − b) to find 27² − 4².
3. 3.If a + b = 14 and ab = 40, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 12².
5. 5.Use (a − b)² = a² − 2ab + b² to find 44².
6. 6.Use (a + b)² = a² + 2ab + b² to find 15².
7. 7.Use (a + b)(a − b) = a² − b² to find 47 × 33.
8. 8.Use (a + b)² = a² + 2ab + b² to find 55².
9. 9.Use (a + b)² = a² + 2ab + b² to find 82².
10. 10.Use (a − b)² = a² − 2ab + b² to find 48².
11. 11.Use (a − b)² = a² − 2ab + b² to find 87².
12. 12.If a + b = 6 and ab = 5, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 4 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 73².
15. 15.Use (a − b)² = a² − 2ab + b² to find 15².
16. 16.Use (a + b)² = a² + 2ab + b² to find 36².
17. 17.Find the value of x² − y² when x = 6 and y = 5.
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 2.
19. 19.Use (a + b)(a − b) = a² − b² to find 67 × 53.
20. 20.Use a² − b² = (a + b)(a − b) to find 63² − 11².
21. 21.If a + b = 14 and ab = 24, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 99 × 81.
23. 23.Use a² − b² = (a + b)(a − b) to find 39² − 7².
24. 24.Use a² − b² = (a + b)(a − b) to find 83² − 72².
25. 25.Use (a − b)² = a² − 2ab + b² to find 78².
26. 26.Use a² − b² = (a + b)(a − b) to find 29² − 23².
27. 27.Find the value of x² + 2xy + y² when x = 7 and y = 2.
28. 28.Use a² − b² = (a + b)(a − b) to find 31² − 10².
29. 29.Use (a + b)² = a² + 2ab + b² to find 96².
30. 30.Use (a + b)² = a² + 2ab + b² to find 56².
31. 31.Use a² − b² = (a + b)(a − b) to find 54² − 35².
32. 32.Find the value of x² − y² when x = 4 and y = 2.
33. 33.Use (a − b)² = a² − 2ab + b² to find 47².
34. 34.Use (a + b)² = a² + 2ab + b² to find 76².
35. 35.Use (a + b)² = a² + 2ab + b² to find 46².
36. 36.Use (a − b)² = a² − 2ab + b² to find 24².
37. 37.If a + b = 16 and ab = 60, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 19².
39. 39.If a + b = 11 and ab = 30, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 10 and y = 4.

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