Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 457 · 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 = 10 and ab = 16, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 68 × 52.
3. 3.Find the value of x² + 2xy + y² when x = 11 and y = 4.
4. 4.If a + b = 5 and ab = 6, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 94².
6. 6.Use a² − b² = (a + b)(a − b) to find 94² − 19².
7. 7.Use (a + b)² = a² + 2ab + b² to find 81².
8. 8.Use (a − b)² = a² − 2ab + b² to find 61².
9. 9.Use (a + b)² = a² + 2ab + b² to find 73².
10. 10.If a − b = 3 and ab = 40, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 68² − 20².
12. 12.Use (a + b)(a − b) = a² − b² to find 104 × 96.
13. 13.Use (a − b)² = a² − 2ab + b² to find 28².
14. 14.Use (a + b)² = a² + 2ab + b² to find 87².
15. 15.Use (a + b)² = a² + 2ab + b² to find 38².
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.If a − b = 6 and ab = 55, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 101 × 99.
19. 19.Use (a + b)² = a² + 2ab + b² to find 76².
20. 20.Use (a + b)² = a² + 2ab + b² to find 22².
21. 21.Find the value of x² − 2xy + y² when x = 12 and y = 7.
22. 22.Use (a + b)(a − b) = a² − b² to find 52 × 48.
23. 23.Use (a + b)² = a² + 2ab + b² to find 78².
24. 24.Find the value of x² − y² when x = 5 and y = 4.
25. 25.Use (a − b)² = a² − 2ab + b² to find 35².
26. 26.Find the value of x² + 2xy + y² when x = 9 and y = 6.
27. 27.Use (a + b)² = a² + 2ab + b² to find 49².
28. 28.Use (a − b)² = a² − 2ab + b² to find 63².
29. 29.Use (a − b)² = a² − 2ab + b² to find 29².
30. 30.Use a² − b² = (a + b)(a − b) to find 31² − 17².
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 44 × 36.
33. 33.If a − b = 11 and ab = 12, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 12².
35. 35.Use a² − b² = (a + b)(a − b) to find 48² − 40².
36. 36.Use (a + b)² = a² + 2ab + b² to find 85².
37. 37.Use (a + b)² = a² + 2ab + b² to find 16².
38. 38.Use (a + b)(a − b) = a² − b² to find 89 × 71.
39. 39.Use a² − b² = (a + b)(a − b) to find 20² − 6².
40. 40.Use (a + b)² = a² + 2ab + b² to find 96².

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