Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 581 · 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)(a − b) = a² − b² to find 89 × 71.
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 38² − 33².
4. 4.Use (a − b)² = a² − 2ab + b² to find 85².
5. 5.Use (a − b)² = a² − 2ab + b² to find 62².
6. 6.Use (a + b)² = a² + 2ab + b² to find 57².
7. 7.Use (a + b)(a − b) = a² − b² to find 61 × 59.
8. 8.Use (a + b)(a − b) = a² − b² to find 59 × 41.
9. 9.If a − b = 8 and ab = 9, what is a² + b²?
10. 10.Find the value of x² − y² when x = 7 and y = 5.
11. 11.Use (a + b)² = a² + 2ab + b² to find 92².
12. 12.Use a² − b² = (a + b)(a − b) to find 80² − 13².
13. 13.Find the value of x² − y² when x = 6 and y = 4.
14. 14.Use (a − b)² = a² − 2ab + b² to find 23².
15. 15.Use a² − b² = (a + b)(a − b) to find 22² − 10².
16. 16.Use (a − b)² = a² − 2ab + b² to find 77².
17. 17.Use (a + b)(a − b) = a² − b² to find 43 × 37.
18. 18.Use (a + b)² = a² + 2ab + b² to find 11².
19. 19.Use a² − b² = (a + b)(a − b) to find 41² − 38².
20. 20.Use (a − b)² = a² − 2ab + b² to find 44².
21. 21.Use (a + b)² = a² + 2ab + b² to find 29².
22. 22.If a − b = 2 and ab = 15, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 81 × 79.
24. 24.Use (a + b)(a − b) = a² − b² to find 32 × 28.
25. 25.If a − b = 4 and ab = 5, what is a² + b²?
26. 26.If a − b = 2 and ab = 48, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 94² − 61².
28. 28.Use a² − b² = (a + b)(a − b) to find 99² − 12².
29. 29.If a − b = 11 and ab = 12, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 92² − 83².
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 3.
32. 32.If a + b = 22 and ab = 120, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 109².
34. 34.Find the value of x² − y² when x = 12 and y = 2.
35. 35.Find the value of x² − 2xy + y² when x = 15 and y = 7.
36. 36.If a + b = 12 and ab = 27, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 24².
38. 38.Use (a − b)² = a² − 2ab + b² to find 75².
39. 39.Find the value of x² − 2xy + y² when x = 14 and y = 7.
40. 40.Use (a − b)² = a² − 2ab + b² to find 16².

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