Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 866 · 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 97².
2. 2.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Use (a + b)² = a² + 2ab + b² to find 44².
4. 4.Use (a + b)² = a² + 2ab + b² to find 83².
5. 5.Use (a − b)² = a² − 2ab + b² to find 49².
6. 6.Find the value of x² + 2xy + y² when x = 11 and y = 1.
7. 7.Use a² − b² = (a + b)(a − b) to find 49² − 30².
8. 8.Use (a − b)² = a² − 2ab + b² to find 74².
9. 9.Use (a + b)² = a² + 2ab + b² to find 107².
10. 10.Use (a + b)(a − b) = a² − b² to find 52 × 48.
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.Use a² − b² = (a + b)(a − b) to find 23² − 16².
13. 13.If a − b = 3 and ab = 10, what is a² + b²?
14. 14.Find the value of x² − 2xy + y² when x = 13 and y = 4.
15. 15.Use a² − b² = (a + b)(a − b) to find 45² − 2².
16. 16.Find the value of x² − y² when x = 9 and y = 2.
17. 17.Use (a + b)² = a² + 2ab + b² to find 58².
18. 18.Use (a + b)² = a² + 2ab + b² to find 46².
19. 19.Find the value of x² − 2xy + y² when x = 13 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 88².
21. 21.If a + b = 15 and ab = 54, what is a² + b²?
22. 22.If a + b = 9 and ab = 18, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 82².
24. 24.Find the value of x² + 2xy + y² when x = 6 and y = 2.
25. 25.Use (a + b)² = a² + 2ab + b² to find 65².
26. 26.Use (a − b)² = a² − 2ab + b² to find 69².
27. 27.Find the value of x² + 2xy + y² when x = 13 and y = 10.
28. 28.Use a² − b² = (a + b)(a − b) to find 53² − 35².
29. 29.Use (a + b)(a − b) = a² − b² to find 48 × 32.
30. 30.Find the value of x² − 2xy + y² when x = 5 and y = 4.
31. 31.Use a² − b² = (a + b)(a − b) to find 34² − 31².
32. 32.Use (a − b)² = a² − 2ab + b² to find 15².
33. 33.Use a² − b² = (a + b)(a − b) to find 34² − 26².
34. 34.Find the value of x² − 2xy + y² when x = 13 and y = 2.
35. 35.Use (a − b)² = a² − 2ab + b² to find 29².
36. 36.Use (a − b)² = a² − 2ab + b² to find 33².
37. 37.Use a² − b² = (a + b)(a − b) to find 52² − 45².
38. 38.Use a² − b² = (a + b)(a − b) to find 85² − 70².
39. 39.Use (a + b)(a − b) = a² − b² to find 64 × 56.
40. 40.Use (a + b)² = a² + 2ab + b² to find 43².

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