Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 355 · 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 94² − 57².
2. 2.Find the value of x² − y² when x = 15 and y = 3.
3. 3.Find the value of x² − y² when x = 14 and y = 3.
4. 4.If a + b = 9 and ab = 14, what is a² + b²?
5. 5.If a − b = 5 and ab = 6, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 9 and y = 6.
7. 7.Use (a + b)(a − b) = a² − b² to find 82 × 78.
8. 8.Use a² − b² = (a + b)(a − b) to find 73² − 14².
9. 9.Use (a + b)(a − b) = a² − b² to find 24 × 16.
10. 10.Use (a − b)² = a² − 2ab + b² to find 48².
11. 11.Use (a + b)² = a² + 2ab + b² to find 72².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 21 × 19.
14. 14.Use a² − b² = (a + b)(a − b) to find 96² − 18².
15. 15.Find the value of x² − 2xy + y² when x = 4 and y = 2.
16. 16.Find the value of x² − 2xy + y² when x = 10 and y = 4.
17. 17.Use a² − b² = (a + b)(a − b) to find 45² − 43².
18. 18.If a − b = 1 and ab = 2, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 51².
20. 20.If a − b = 5 and ab = 36, what is a² + b²?
21. 21.If a + b = 8 and ab = 15, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 15².
23. 23.Use (a + b)² = a² + 2ab + b² to find 104².
24. 24.Use (a + b)² = a² + 2ab + b² to find 62².
25. 25.Find the value of x² + 2xy + y² when x = 4 and y = 1.
26. 26.Use (a + b)² = a² + 2ab + b² to find 106².
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 1.
28. 28.Use (a + b)² = a² + 2ab + b² to find 17².
29. 29.Use (a + b)(a − b) = a² − b² to find 105 × 95.
30. 30.Use (a + b)(a − b) = a² − b² to find 83 × 77.
31. 31.Use a² − b² = (a + b)(a − b) to find 77² − 10².
32. 32.If a − b = 10 and ab = 11, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 61² − 42².
34. 34.Use (a − b)² = a² − 2ab + b² to find 34².
35. 35.Use (a + b)(a − b) = a² − b² to find 65 × 55.
36. 36.Use a² − b² = (a + b)(a − b) to find 68² − 33².
37. 37.Use (a − b)² = a² − 2ab + b² to find 93².
38. 38.Find the value of x² − 2xy + y² when x = 4 and y = 3.
39. 39.Use (a + b)² = a² + 2ab + b² to find 96².
40. 40.Use a² − b² = (a + b)(a − b) to find 47² − 8².

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