Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 876 · 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 a² − b² = (a + b)(a − b) to find 48² − 23².
2. 2.Use (a − b)² = a² − 2ab + b² to find 38².
3. 3.Use (a + b)(a − b) = a² − b² to find 63 × 57.
4. 4.Use (a + b)² = a² + 2ab + b² to find 86².
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 6.
6. 6.Use (a − b)² = a² − 2ab + b² to find 62².
7. 7.Find the value of x² − y² when x = 4 and y = 1.
8. 8.Use (a + b)² = a² + 2ab + b² to find 96².
9. 9.Use (a − b)² = a² − 2ab + b² to find 63².
10. 10.Use (a + b)(a − b) = a² − b² to find 99 × 81.
11. 11.Use (a + b)² = a² + 2ab + b² to find 104².
12. 12.Use (a + b)(a − b) = a² − b² to find 32 × 28.
13. 13.Find the value of x² + 2xy + y² when x = 6 and y = 3.
14. 14.Use (a − b)² = a² − 2ab + b² to find 91².
15. 15.Use (a + b)(a − b) = a² − b² to find 102 × 98.
16. 16.Use a² − b² = (a + b)(a − b) to find 71² − 49².
17. 17.Use a² − b² = (a + b)(a − b) to find 46² − 39².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 4.
19. 19.Use a² − b² = (a + b)(a − b) to find 81² − 39².
20. 20.Use (a − b)² = a² − 2ab + b² to find 16².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 65².
23. 23.Use (a + b)(a − b) = a² − b² to find 82 × 78.
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Find the value of x² − 2xy + y² when x = 10 and y = 5.
26. 26.If a + b = 8 and ab = 15, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 66².
28. 28.Use (a + b)(a − b) = a² − b² to find 71 × 69.
29. 29.Use (a − b)² = a² − 2ab + b² to find 79².
30. 30.Use a² − b² = (a + b)(a − b) to find 73² − 42².
31. 31.Use (a − b)² = a² − 2ab + b² to find 33².
32. 32.If a + b = 4 and ab = 3, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 5 and y = 1.
34. 34.Find the value of x² + 2xy + y² when x = 5 and y = 2.
35. 35.Use (a + b)(a − b) = a² − b² to find 49 × 31.
36. 36.If a + b = 11 and ab = 24, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 71².
38. 38.Use (a + b)(a − b) = a² − b² to find 57 × 43.
39. 39.Use (a − b)² = a² − 2ab + b² to find 76².
40. 40.Use (a + b)² = a² + 2ab + b² to find 13².

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