Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 302 · 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 = 13 and y = 2.
2. 2.If a + b = 15 and ab = 56, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 23².
4. 4.Use a² − b² = (a + b)(a − b) to find 55² − 17².
5. 5.Use (a − b)² = a² − 2ab + b² to find 23².
6. 6.Use (a − b)² = a² − 2ab + b² to find 79².
7. 7.Find the value of x² + 2xy + y² when x = 3 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 52².
10. 10.Use (a + b)² = a² + 2ab + b² to find 16².
11. 11.Use (a + b)² = a² + 2ab + b² to find 63².
12. 12.Find the value of x² − 2xy + y² when x = 10 and y = 7.
13. 13.Use (a + b)² = a² + 2ab + b² to find 56².
14. 14.Use a² − b² = (a + b)(a − b) to find 89² − 28².
15. 15.If a + b = 9 and ab = 20, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 83 × 77.
17. 17.If a + b = 5 and ab = 6, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 47² − 20².
19. 19.Find the value of x² − 2xy + y² when x = 12 and y = 8.
20. 20.Use a² − b² = (a + b)(a − b) to find 89² − 51².
21. 21.Use a² − b² = (a + b)(a − b) to find 79² − 16².
22. 22.Use (a + b)² = a² + 2ab + b² to find 82².
23. 23.If a − b = 2 and ab = 63, what is a² + b²?
24. 24.If a − b = 1 and ab = 6, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 6 and y = 1.
26. 26.Use a² − b² = (a + b)(a − b) to find 34² − 5².
27. 27.Use (a + b)(a − b) = a² − b² to find 47 × 33.
28. 28.Use (a − b)² = a² − 2ab + b² to find 69².
29. 29.Use (a + b)(a − b) = a² − b² to find 59 × 41.
30. 30.Use (a + b)(a − b) = a² − b² to find 24 × 16.
31. 31.Use (a + b)(a − b) = a² − b² to find 81 × 79.
32. 32.Use (a + b)² = a² + 2ab + b² to find 73².
33. 33.Use (a + b)(a − b) = a² − b² to find 99 × 81.
34. 34.Use (a − b)² = a² − 2ab + b² to find 83².
35. 35.If a + b = 5 and ab = 4, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 33².
37. 37.If a − b = 3 and ab = 4, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 93 × 87.
39. 39.Use a² − b² = (a + b)(a − b) to find 32² − 6².
40. 40.Use a² − b² = (a + b)(a − b) to find 61² − 4².

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