Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 233 · 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 83².
2. 2.Find the value of x² − y² when x = 15 and y = 7.
3. 3.Use (a + b)(a − b) = a² − b² to find 43 × 37.
4. 4.Use (a + b)(a − b) = a² − b² to find 96 × 84.
5. 5.Use (a + b)² = a² + 2ab + b² to find 22².
6. 6.Use (a − b)² = a² − 2ab + b² to find 37².
7. 7.Use a² − b² = (a + b)(a − b) to find 76² − 39².
8. 8.Use (a − b)² = a² − 2ab + b² to find 52².
9. 9.Find the value of x² + 2xy + y² when x = 13 and y = 5.
10. 10.Use (a − b)² = a² − 2ab + b² to find 22².
11. 11.Use (a + b)² = a² + 2ab + b² to find 15².
12. 12.If a + b = 11 and ab = 28, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 22 × 18.
14. 14.Find the value of x² − y² when x = 4 and y = 2.
15. 15.If a + b = 13 and ab = 22, what is a² + b²?
16. 16.If a + b = 8 and ab = 7, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 30² − 2².
18. 18.If a − b = 8 and ab = 33, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 42 × 38.
20. 20.Use (a + b)(a − b) = a² − b² to find 82 × 78.
21. 21.Use (a − b)² = a² − 2ab + b² to find 16².
22. 22.Use (a − b)² = a² − 2ab + b² to find 19².
23. 23.Use (a + b)² = a² + 2ab + b² to find 47².
24. 24.Use (a + b)² = a² + 2ab + b² to find 92².
25. 25.If a + b = 15 and ab = 56, what is a² + b²?
26. 26.If a + b = 15 and ab = 50, what is a² + b²?
27. 27.Find the value of x² − y² when x = 9 and y = 7.
28. 28.If a − b = 3 and ab = 28, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 62².
30. 30.Use (a + b)² = a² + 2ab + b² to find 107².
31. 31.Use (a − b)² = a² − 2ab + b² to find 77².
32. 32.Use (a + b)(a − b) = a² − b² to find 71 × 69.
33. 33.Use (a − b)² = a² − 2ab + b² to find 47².
34. 34.Use (a + b)² = a² + 2ab + b² to find 108².
35. 35.Use (a + b)(a − b) = a² − b² to find 29 × 11.
36. 36.Use a² − b² = (a + b)(a − b) to find 43² − 26².
37. 37.Use (a + b)² = a² + 2ab + b² to find 69².
38. 38.If a + b = 5 and ab = 4, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 83².
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 1.

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