Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 144 · 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.If a − b = 4 and ab = 45, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 12 and y = 1.
3. 3.Use (a + b)² = a² + 2ab + b² to find 41².
4. 4.Use (a + b)(a − b) = a² − b² to find 76 × 64.
5. 5.Use (a + b)² = a² + 2ab + b² to find 39².
6. 6.Use a² − b² = (a + b)(a − b) to find 98² − 42².
7. 7.Use (a + b)² = a² + 2ab + b² to find 86².
8. 8.Use (a + b)² = a² + 2ab + b² to find 65².
9. 9.Use (a − b)² = a² − 2ab + b² to find 82².
10. 10.Use (a + b)² = a² + 2ab + b² to find 13².
11. 11.Use a² − b² = (a + b)(a − b) to find 45² − 1².
12. 12.Find the value of x² − 2xy + y² when x = 13 and y = 6.
13. 13.Find the value of x² − y² when x = 9 and y = 8.
14. 14.Use (a − b)² = a² − 2ab + b² to find 92².
15. 15.Find the value of x² + 2xy + y² when x = 13 and y = 12.
16. 16.Use (a − b)² = a² − 2ab + b² to find 48².
17. 17.Use (a + b)(a − b) = a² − b² to find 35 × 25.
18. 18.Use (a + b)² = a² + 2ab + b² to find 54².
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 38² − 19².
21. 21.Use (a − b)² = a² − 2ab + b² to find 58².
22. 22.Use a² − b² = (a + b)(a − b) to find 31² − 18².
23. 23.Find the value of x² − y² when x = 6 and y = 3.
24. 24.Use a² − b² = (a + b)(a − b) to find 54² − 6².
25. 25.Use (a + b)² = a² + 2ab + b² to find 21².
26. 26.Use (a + b)² = a² + 2ab + b² to find 58².
27. 27.Use (a − b)² = a² − 2ab + b² to find 12².
28. 28.Find the value of x² + 2xy + y² when x = 14 and y = 11.
29. 29.Use (a − b)² = a² − 2ab + b² to find 28².
30. 30.Use (a + b)² = a² + 2ab + b² to find 45².
31. 31.Use a² − b² = (a + b)(a − b) to find 92² − 82².
32. 32.Find the value of x² − y² when x = 11 and y = 4.
33. 33.Use (a + b)² = a² + 2ab + b² to find 22².
34. 34.Use (a − b)² = a² − 2ab + b² to find 49².
35. 35.Use a² − b² = (a + b)(a − b) to find 82² − 49².
36. 36.Use (a + b)² = a² + 2ab + b² to find 56².
37. 37.If a − b = 6 and ab = 27, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 47 × 33.
39. 39.Use (a − b)² = a² − 2ab + b² to find 72².
40. 40.Use (a + b)(a − b) = a² − b² to find 105 × 95.

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