Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 543 · 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 (a − b)² = a² − 2ab + b² to find 85².
2. 2.If a − b = 2 and ab = 3, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 58².
4. 4.Use a² − b² = (a + b)(a − b) to find 88² − 74².
5. 5.Use (a − b)² = a² − 2ab + b² to find 16².
6. 6.If a − b = 3 and ab = 108, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 2.
8. 8.Find the value of x² + 2xy + y² when x = 5 and y = 1.
9. 9.Use a² − b² = (a + b)(a − b) to find 89² − 16².
10. 10.Find the value of x² − 2xy + y² when x = 14 and y = 6.
11. 11.Use (a + b)² = a² + 2ab + b² to find 61².
12. 12.Use a² − b² = (a + b)(a − b) to find 58² − 47².
13. 13.If a + b = 20 and ab = 96, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 71².
15. 15.Use a² − b² = (a + b)(a − b) to find 72² − 6².
16. 16.Use (a + b)² = a² + 2ab + b² to find 52².
17. 17.Use (a − b)² = a² − 2ab + b² to find 37².
18. 18.Use (a + b)² = a² + 2ab + b² to find 58².
19. 19.Use (a + b)² = a² + 2ab + b² to find 73².
20. 20.Use (a − b)² = a² − 2ab + b² to find 71².
21. 21.Use (a − b)² = a² − 2ab + b² to find 88².
22. 22.If a + b = 9 and ab = 18, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 63² − 49².
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 2.
25. 25.Use (a − b)² = a² − 2ab + b² to find 39².
26. 26.Use a² − b² = (a + b)(a − b) to find 96² − 62².
27. 27.Use a² − b² = (a + b)(a − b) to find 61² − 23².
28. 28.Use (a + b)² = a² + 2ab + b² to find 14².
29. 29.Use (a + b)² = a² + 2ab + b² to find 13².
30. 30.Use (a + b)² = a² + 2ab + b² to find 94².
31. 31.Use (a + b)² = a² + 2ab + b² to find 95².
32. 32.Find the value of x² − 2xy + y² when x = 7 and y = 4.
33. 33.If a + b = 21 and ab = 110, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 28 × 12.
35. 35.Use (a − b)² = a² − 2ab + b² to find 65².
36. 36.Use (a − b)² = a² − 2ab + b² to find 62².
37. 37.Use (a − b)² = a² − 2ab + b² to find 19².
38. 38.Use a² − b² = (a + b)(a − b) to find 29² − 4².
39. 39.Use a² − b² = (a + b)(a − b) to find 29² − 5².
40. 40.Use a² − b² = (a + b)(a − b) to find 68² − 49².

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