Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 951 · 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 55².
2. 2.Use (a − b)² = a² − 2ab + b² to find 46².
3. 3.Find the value of x² − y² when x = 4 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 51².
5. 5.Use a² − b² = (a + b)(a − b) to find 57² − 15².
6. 6.Find the value of x² − 2xy + y² when x = 6 and y = 5.
7. 7.Use a² − b² = (a + b)(a − b) to find 64² − 2².
8. 8.If a − b = 8 and ab = 33, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 19².
10. 10.Use (a + b)(a − b) = a² − b² to find 68 × 52.
11. 11.If a + b = 5 and ab = 6, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 68².
13. 13.Find the value of x² − 2xy + y² when x = 14 and y = 13.
14. 14.Use (a − b)² = a² − 2ab + b² to find 72².
15. 15.Use (a − b)² = a² − 2ab + b² to find 57².
16. 16.Use a² − b² = (a + b)(a − b) to find 38² − 30².
17. 17.Use (a + b)² = a² + 2ab + b² to find 12².
18. 18.Use (a + b)(a − b) = a² − b² to find 34 × 26.
19. 19.If a + b = 17 and ab = 72, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 22² − 5².
21. 21.Use (a − b)² = a² − 2ab + b² to find 82².
22. 22.Find the value of x² + 2xy + y² when x = 7 and y = 2.
23. 23.Use a² − b² = (a + b)(a − b) to find 71² − 22².
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.Find the value of x² + 2xy + y² when x = 13 and y = 12.
26. 26.Use (a + b)² = a² + 2ab + b² to find 21².
27. 27.Find the value of x² − y² when x = 12 and y = 7.
28. 28.Find the value of x² − y² when x = 14 and y = 3.
29. 29.Use (a + b)(a − b) = a² − b² to find 69 × 51.
30. 30.Find the value of x² − 2xy + y² when x = 7 and y = 5.
31. 31.Use (a + b)² = a² + 2ab + b² to find 28².
32. 32.Find the value of x² − y² when x = 12 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 18².
34. 34.If a + b = 9 and ab = 14, what is a² + b²?
35. 35.Find the value of x² + 2xy + y² when x = 12 and y = 9.
36. 36.Find the value of x² + 2xy + y² when x = 13 and y = 2.
37. 37.Use (a − b)² = a² − 2ab + b² to find 58².
38. 38.Use (a − b)² = a² − 2ab + b² to find 17².
39. 39.Find the value of x² + 2xy + y² when x = 8 and y = 6.
40. 40.Use (a + b)(a − b) = a² − b² to find 31 × 29.

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