Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 441 · 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 a² − b² = (a + b)(a − b) to find 54² − 6².
2. 2.Use (a + b)² = a² + 2ab + b² to find 76².
3. 3.Use (a − b)² = a² − 2ab + b² to find 48².
4. 4.Use (a − b)² = a² − 2ab + b² to find 31².
5. 5.Find the value of x² + 2xy + y² when x = 8 and y = 5.
6. 6.If a + b = 5 and ab = 4, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 12².
8. 8.Use (a + b)² = a² + 2ab + b² to find 39².
9. 9.Use (a − b)² = a² − 2ab + b² to find 55².
10. 10.Use a² − b² = (a + b)(a − b) to find 34² − 28².
11. 11.Use (a + b)(a − b) = a² − b² to find 79 × 61.
12. 12.If a + b = 15 and ab = 56, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 80² − 20².
14. 14.Use (a − b)² = a² − 2ab + b² to find 84².
15. 15.If a + b = 6 and ab = 5, what is a² + b²?
16. 16.If a − b = 1 and ab = 6, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 29 × 11.
18. 18.Use a² − b² = (a + b)(a − b) to find 31² − 14².
19. 19.Use (a + b)(a − b) = a² − b² to find 45 × 35.
20. 20.If a + b = 8 and ab = 12, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 7 and y = 3.
22. 22.Find the value of x² − 2xy + y² when x = 12 and y = 1.
23. 23.Use (a − b)² = a² − 2ab + b² to find 39².
24. 24.Find the value of x² − 2xy + y² when x = 3 and y = 2.
25. 25.Use (a + b)(a − b) = a² − b² to find 101 × 99.
26. 26.Use (a + b)² = a² + 2ab + b² to find 108².
27. 27.Use (a − b)² = a² − 2ab + b² to find 99².
28. 28.Use (a + b)(a − b) = a² − b² to find 36 × 24.
29. 29.Use (a + b)² = a² + 2ab + b² to find 103².
30. 30.Use (a + b)² = a² + 2ab + b² to find 57².
31. 31.Use (a − b)² = a² − 2ab + b² to find 12².
32. 32.Use (a + b)² = a² + 2ab + b² to find 52².
33. 33.Use a² − b² = (a + b)(a − b) to find 31² − 25².
34. 34.Use a² − b² = (a + b)(a − b) to find 64² − 2².
35. 35.Use a² − b² = (a + b)(a − b) to find 23² − 6².
36. 36.Use (a + b)(a − b) = a² − b² to find 64 × 56.
37. 37.Use a² − b² = (a + b)(a − b) to find 83² − 51².
38. 38.Find the value of x² + 2xy + y² when x = 10 and y = 6.
39. 39.Use (a − b)² = a² − 2ab + b² to find 24².
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 11².

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