Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 682 · 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 35².
2. 2.Use (a − b)² = a² − 2ab + b² to find 37².
3. 3.Find the value of x² − y² when x = 5 and y = 3.
4. 4.Use (a − b)² = a² − 2ab + b² to find 92².
5. 5.If a − b = 1 and ab = 2, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 95 × 85.
7. 7.Use (a − b)² = a² − 2ab + b² to find 79².
8. 8.Use (a + b)(a − b) = a² − b² to find 98 × 82.
9. 9.Find the value of x² + 2xy + y² when x = 12 and y = 4.
10. 10.Use (a + b)² = a² + 2ab + b² to find 75².
11. 11.Use (a + b)² = a² + 2ab + b² to find 105².
12. 12.Use (a + b)² = a² + 2ab + b² to find 56².
13. 13.Find the value of x² + 2xy + y² when x = 7 and y = 5.
14. 14.Find the value of x² − y² when x = 3 and y = 1.
15. 15.Use (a − b)² = a² − 2ab + b² to find 43².
16. 16.Use (a + b)² = a² + 2ab + b² to find 86².
17. 17.Use (a + b)² = a² + 2ab + b² to find 62².
18. 18.Find the value of x² − 2xy + y² when x = 6 and y = 5.
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 41² − 9².
21. 21.Use (a − b)² = a² − 2ab + b² to find 28².
22. 22.Use (a + b)² = a² + 2ab + b² to find 23².
23. 23.Find the value of x² − y² when x = 11 and y = 5.
24. 24.Use (a + b)² = a² + 2ab + b² to find 61².
25. 25.Use a² − b² = (a + b)(a − b) to find 60² − 2².
26. 26.Use (a − b)² = a² − 2ab + b² to find 97².
27. 27.Find the value of x² + 2xy + y² when x = 3 and y = 2.
28. 28.Find the value of x² − 2xy + y² when x = 14 and y = 2.
29. 29.Find the value of x² − y² when x = 15 and y = 14.
30. 30.Use (a + b)(a − b) = a² − b² to find 27 × 13.
31. 31.Use (a + b)² = a² + 2ab + b² to find 91².
32. 32.If a + b = 9 and ab = 8, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 77².
34. 34.Use (a + b)(a − b) = a² − b² to find 44 × 36.
35. 35.Use a² − b² = (a + b)(a − b) to find 20² − 2².
36. 36.Find the value of x² − y² when x = 14 and y = 2.
37. 37.Use a² − b² = (a + b)(a − b) to find 73² − 7².
38. 38.If a − b = 7 and ab = 30, what is a² + b²?
39. 39.If a − b = 6 and ab = 27, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 47 × 33.

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