Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 923 · 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 50² − 24².
2. 2.Use (a − b)² = a² − 2ab + b² to find 59².
3. 3.Use a² − b² = (a + b)(a − b) to find 59² − 36².
4. 4.If a − b = 2 and ab = 48, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 13².
6. 6.Use (a + b)(a − b) = a² − b² to find 99 × 81.
7. 7.Find the value of x² − y² when x = 4 and y = 2.
8. 8.Use a² − b² = (a + b)(a − b) to find 60² − 10².
9. 9.If a − b = 8 and ab = 9, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 17².
11. 11.Use (a − b)² = a² − 2ab + b² to find 54².
12. 12.Find the value of x² − 2xy + y² when x = 14 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 14².
14. 14.Use (a − b)² = a² − 2ab + b² to find 49².
15. 15.Use a² − b² = (a + b)(a − b) to find 22² − 18².
16. 16.Find the value of x² + 2xy + y² when x = 7 and y = 2.
17. 17.If a + b = 13 and ab = 12, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 87².
19. 19.Use (a + b)(a − b) = a² − b² to find 81 × 79.
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 49².
22. 22.Use (a − b)² = a² − 2ab + b² to find 97².
23. 23.Use (a + b)² = a² + 2ab + b² to find 86².
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 2.
25. 25.If a + b = 4 and ab = 3, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 89² − 52².
27. 27.If a + b = 15 and ab = 54, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 48².
29. 29.Use (a − b)² = a² − 2ab + b² to find 46².
30. 30.If a − b = 7 and ab = 8, what is a² + b²?
31. 31.Find the value of x² − 2xy + y² when x = 14 and y = 13.
32. 32.Find the value of x² − 2xy + y² when x = 7 and y = 2.
33. 33.Find the value of x² − 2xy + y² when x = 9 and y = 3.
34. 34.Use (a + b)(a − b) = a² − b² to find 44 × 36.
35. 35.Use (a + b)² = a² + 2ab + b² to find 102².
36. 36.Use (a − b)² = a² − 2ab + b² to find 85².
37. 37.Use (a + b)² = a² + 2ab + b² to find 39².
38. 38.Use a² − b² = (a + b)(a − b) to find 88² − 81².
39. 39.Use (a + b)² = a² + 2ab + b² to find 101².
40. 40.Use (a − b)² = a² − 2ab + b² to find 96².

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