Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 111 · 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 73².
2. 2.Use (a − b)² = a² − 2ab + b² to find 26².
3. 3.Use (a − b)² = a² − 2ab + b² to find 36².
4. 4.Use a² − b² = (a + b)(a − b) to find 63² − 14².
5. 5.Use (a + b)² = a² + 2ab + b² to find 64².
6. 6.Use (a − b)² = a² − 2ab + b² to find 58².
7. 7.If a − b = 8 and ab = 20, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 58².
9. 9.If a + b = 16 and ab = 60, what is a² + b²?
10. 10.Find the value of x² − y² when x = 5 and y = 1.
11. 11.Use (a + b)² = a² + 2ab + b² to find 72².
12. 12.If a − b = 8 and ab = 48, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 59².
14. 14.Use (a + b)² = a² + 2ab + b² to find 56².
15. 15.Use (a + b)² = a² + 2ab + b² to find 43².
16. 16.If a − b = 7 and ab = 44, what is a² + b²?
17. 17.If a − b = 1 and ab = 6, what is a² + b²?
18. 18.Find the value of x² − y² when x = 6 and y = 1.
19. 19.If a + b = 14 and ab = 48, what is a² + b²?
20. 20.Find the value of x² − 2xy + y² when x = 4 and y = 1.
21. 21.If a − b = 1 and ab = 42, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 33².
23. 23.Use (a − b)² = a² − 2ab + b² to find 39².
24. 24.Find the value of x² − y² when x = 8 and y = 6.
25. 25.Use a² − b² = (a + b)(a − b) to find 90² − 73².
26. 26.Use (a + b)² = a² + 2ab + b² to find 15².
27. 27.If a + b = 14 and ab = 45, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 46 × 34.
29. 29.Use (a + b)² = a² + 2ab + b² to find 55².
30. 30.If a − b = 2 and ab = 63, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 75 × 65.
32. 32.Use (a − b)² = a² − 2ab + b² to find 28².
33. 33.Use a² − b² = (a + b)(a − b) to find 36² − 10².
34. 34.Use a² − b² = (a + b)(a − b) to find 35² − 7².
35. 35.Use (a − b)² = a² − 2ab + b² to find 94².
36. 36.Use (a − b)² = a² − 2ab + b² to find 16².
37. 37.Use (a + b)(a − b) = a² − b² to find 69 × 51.
38. 38.Use (a − b)² = a² − 2ab + b² to find 93².
39. 39.If a − b = 2 and ab = 3, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 14 and y = 7.

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