Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 279 · 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.Find the value of x² − y² when x = 3 and y = 2.
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 66².
4. 4.Use a² − b² = (a + b)(a − b) to find 40² − 23².
5. 5.Find the value of x² + 2xy + y² when x = 4 and y = 1.
6. 6.Use a² − b² = (a + b)(a − b) to find 23² − 19².
7. 7.Find the value of x² − 2xy + y² when x = 12 and y = 3.
8. 8.Use (a − b)² = a² − 2ab + b² to find 17².
9. 9.Find the value of x² − 2xy + y² when x = 5 and y = 4.
10. 10.Find the value of x² + 2xy + y² when x = 7 and y = 1.
11. 11.Use (a + b)² = a² + 2ab + b² to find 52².
12. 12.Use (a + b)² = a² + 2ab + b² to find 59².
13. 13.Use (a + b)(a − b) = a² − b² to find 83 × 77.
14. 14.Find the value of x² − y² when x = 5 and y = 2.
15. 15.Use (a + b)² = a² + 2ab + b² to find 76².
16. 16.Use (a + b)(a − b) = a² − b² to find 102 × 98.
17. 17.Use a² − b² = (a + b)(a − b) to find 95² − 61².
18. 18.Use (a − b)² = a² − 2ab + b² to find 33².
19. 19.If a + b = 8 and ab = 7, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 10 and y = 4.
21. 21.If a − b = 3 and ab = 88, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 43 × 37.
23. 23.Use a² − b² = (a + b)(a − b) to find 99² − 86².
24. 24.Find the value of x² − 2xy + y² when x = 12 and y = 6.
25. 25.Find the value of x² − y² when x = 5 and y = 1.
26. 26.Use (a + b)² = a² + 2ab + b² to find 11².
27. 27.Use a² − b² = (a + b)(a − b) to find 80² − 61².
28. 28.Use (a + b)(a − b) = a² − b² to find 61 × 59.
29. 29.If a − b = 2 and ab = 35, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 89².
31. 31.Use (a − b)² = a² − 2ab + b² to find 11².
32. 32.Use (a − b)² = a² − 2ab + b² to find 67².
33. 33.If a − b = 1 and ab = 110, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 11 and y = 9.
35. 35.Use (a − b)² = a² − 2ab + b² to find 42².
36. 36.If a + b = 5 and ab = 6, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 95².
38. 38.Use (a + b)(a − b) = a² − b² to find 22 × 18.
39. 39.Find the value of x² − 2xy + y² when x = 11 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 73².

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