Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 277 · 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 66² − 29².
2. 2.Find the value of x² − 2xy + y² when x = 6 and y = 5.
3. 3.Use (a + b)² = a² + 2ab + b² to find 15².
4. 4.Use (a − b)² = a² − 2ab + b² to find 82².
5. 5.If a − b = 3 and ab = 18, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 20² − 19².
7. 7.Use (a − b)² = a² − 2ab + b² to find 83².
8. 8.Use (a + b)² = a² + 2ab + b² to find 85².
9. 9.Use a² − b² = (a + b)(a − b) to find 33² − 24².
10. 10.Find the value of x² + 2xy + y² when x = 9 and y = 1.
11. 11.Find the value of x² − y² when x = 7 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 25² − 7².
13. 13.Use (a + b)² = a² + 2ab + b² to find 68².
14. 14.Find the value of x² + 2xy + y² when x = 10 and y = 6.
15. 15.Use a² − b² = (a + b)(a − b) to find 86² − 13².
16. 16.Use (a − b)² = a² − 2ab + b² to find 71².
17. 17.Use (a + b)(a − b) = a² − b² to find 95 × 85.
18. 18.Use (a + b)(a − b) = a² − b² to find 83 × 77.
19. 19.Use (a + b)² = a² + 2ab + b² to find 88².
20. 20.Use (a + b)(a − b) = a² − b² to find 44 × 36.
21. 21.Find the value of x² − 2xy + y² when x = 7 and y = 4.
22. 22.Use a² − b² = (a + b)(a − b) to find 68² − 62².
23. 23.Find the value of x² − 2xy + y² when x = 6 and y = 3.
24. 24.Use (a + b)(a − b) = a² − b² to find 23 × 17.
25. 25.Use (a + b)² = a² + 2ab + b² to find 82².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 26².
28. 28.Find the value of x² − y² when x = 10 and y = 2.
29. 29.Use (a + b)(a − b) = a² − b² to find 58 × 42.
30. 30.Use (a + b)² = a² + 2ab + b² to find 52².
31. 31.Use a² − b² = (a + b)(a − b) to find 72² − 56².
32. 32.If a + b = 15 and ab = 56, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 81² − 51².
34. 34.Use (a + b)² = a² + 2ab + b² to find 37².
35. 35.Find the value of x² + 2xy + y² when x = 6 and y = 1.
36. 36.Find the value of x² − 2xy + y² when x = 14 and y = 4.
37. 37.Use a² − b² = (a + b)(a − b) to find 97² − 63².
38. 38.Use a² − b² = (a + b)(a − b) to find 84² − 62².
39. 39.Use (a + b)² = a² + 2ab + b² to find 45².
40. 40.Find the value of x² − 2xy + y² when x = 12 and y = 3.

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