Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 447 · 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)(a − b) = a² − b² to find 24 × 16.
2. 2.Find the value of x² − 2xy + y² when x = 6 and y = 1.
3. 3.Use (a + b)² = a² + 2ab + b² to find 52².
4. 4.If a − b = 1 and ab = 2, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 44² − 1².
6. 6.If a + b = 11 and ab = 28, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 69² − 28².
8. 8.Use a² − b² = (a + b)(a − b) to find 46² − 28².
9. 9.Use a² − b² = (a + b)(a − b) to find 88² − 17².
10. 10.Use a² − b² = (a + b)(a − b) to find 96² − 31².
11. 11.Use (a + b)(a − b) = a² − b² to find 44 × 36.
12. 12.Use (a + b)(a − b) = a² − b² to find 57 × 43.
13. 13.Use (a + b)² = a² + 2ab + b² to find 105².
14. 14.Find the value of x² − y² when x = 7 and y = 1.
15. 15.Find the value of x² − y² when x = 11 and y = 8.
16. 16.Use (a − b)² = a² − 2ab + b² to find 76².
17. 17.If a + b = 5 and ab = 4, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 39 × 21.
19. 19.Use a² − b² = (a + b)(a − b) to find 93² − 16².
20. 20.If a + b = 16 and ab = 55, what is a² + b²?
21. 21.If a − b = 3 and ab = 10, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 56².
23. 23.Use a² − b² = (a + b)(a − b) to find 57² − 24².
24. 24.Use (a + b)(a − b) = a² − b² to find 28 × 12.
25. 25.Use (a − b)² = a² − 2ab + b² to find 39².
26. 26.Use (a + b)(a − b) = a² − b² to find 82 × 78.
27. 27.Use (a + b)² = a² + 2ab + b² to find 45².
28. 28.Find the value of x² + 2xy + y² when x = 6 and y = 3.
29. 29.If a + b = 3 and ab = 2, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 73².
31. 31.Use a² − b² = (a + b)(a − b) to find 22² − 2².
32. 32.Use a² − b² = (a + b)(a − b) to find 78² − 22².
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.Use (a − b)² = a² − 2ab + b² to find 44².
35. 35.Use (a − b)² = a² − 2ab + b² to find 42².
36. 36.Use a² − b² = (a + b)(a − b) to find 65² − 31².
37. 37.Use (a + b)² = a² + 2ab + b² to find 64².
38. 38.If a + b = 7 and ab = 12, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 38² − 7².
40. 40.If a + b = 9 and ab = 8, what is a² + b²?

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