Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 422 · 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 + 2xy + y² when x = 15 and y = 12.
2. 2.Find the value of x² + 2xy + y² when x = 6 and y = 3.
3. 3.Use (a − b)² = a² − 2ab + b² to find 19².
4. 4.If a − b = 3 and ab = 4, what is a² + b²?
5. 5.If a − b = 4 and ab = 96, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 45².
7. 7.Use (a + b)(a − b) = a² − b² to find 74 × 66.
8. 8.Find the value of x² − y² when x = 8 and y = 5.
9. 9.Use (a + b)² = a² + 2ab + b² to find 15².
10. 10.Use (a − b)² = a² − 2ab + b² to find 96².
11. 11.Use (a − b)² = a² − 2ab + b² to find 16².
12. 12.Use (a + b)² = a² + 2ab + b² to find 82².
13. 13.Use (a + b)(a − b) = a² − b² to find 22 × 18.
14. 14.Find the value of x² − y² when x = 14 and y = 6.
15. 15.If a − b = 7 and ab = 18, what is a² + b²?
16. 16.If a + b = 5 and ab = 6, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 12 and y = 1.
18. 18.Use (a + b)(a − b) = a² − b² to find 73 × 67.
19. 19.Use a² − b² = (a + b)(a − b) to find 80² − 47².
20. 20.Use a² − b² = (a + b)(a − b) to find 33² − 32².
21. 21.Use (a − b)² = a² − 2ab + b² to find 18².
22. 22.Use (a + b)² = a² + 2ab + b² to find 83².
23. 23.Find the value of x² + 2xy + y² when x = 6 and y = 5.
24. 24.Use (a − b)² = a² − 2ab + b² to find 71².
25. 25.Use (a + b)² = a² + 2ab + b² to find 35².
26. 26.Use (a − b)² = a² − 2ab + b² to find 92².
27. 27.If a − b = 11 and ab = 12, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 75².
29. 29.Use (a + b)(a − b) = a² − b² to find 25 × 15.
30. 30.Use (a + b)² = a² + 2ab + b² to find 101².
31. 31.Use (a + b)(a − b) = a² − b² to find 45 × 35.
32. 32.Use a² − b² = (a + b)(a − b) to find 44² − 34².
33. 33.Use (a + b)² = a² + 2ab + b² to find 88².
34. 34.Use (a + b)² = a² + 2ab + b² to find 79².
35. 35.Use (a + b)(a − b) = a² − b² to find 51 × 49.
36. 36.Use (a + b)² = a² + 2ab + b² to find 31².
37. 37.Use (a − b)² = a² − 2ab + b² to find 23².
38. 38.Use a² − b² = (a + b)(a − b) to find 83² − 6².
39. 39.Use a² − b² = (a + b)(a − b) to find 58² − 43².
40. 40.Use (a + b)(a − b) = a² − b² to find 41 × 39.

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