Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 636 · 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 65².
2. 2.Use (a + b)² = a² + 2ab + b² to find 33².
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Use a² − b² = (a + b)(a − b) to find 85² − 20².
5. 5.Use (a + b)(a − b) = a² − b² to find 23 × 17.
6. 6.If a − b = 3 and ab = 10, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 94² − 57².
8. 8.If a + b = 11 and ab = 24, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 44².
10. 10.Use (a − b)² = a² − 2ab + b² to find 66².
11. 11.Use (a − b)² = a² − 2ab + b² to find 97².
12. 12.If a + b = 5 and ab = 6, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 49².
14. 14.If a + b = 6 and ab = 5, what is a² + b²?
15. 15.If a − b = 1 and ab = 2, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 31² − 1².
17. 17.Use (a − b)² = a² − 2ab + b² to find 47².
18. 18.Use (a − b)² = a² − 2ab + b² to find 73².
19. 19.Use (a + b)² = a² + 2ab + b² to find 76².
20. 20.Find the value of x² + 2xy + y² when x = 11 and y = 2.
21. 21.Find the value of x² − 2xy + y² when x = 8 and y = 3.
22. 22.Use (a − b)² = a² − 2ab + b² to find 83².
23. 23.Use a² − b² = (a + b)(a − b) to find 22² − 19².
24. 24.Use (a + b)² = a² + 2ab + b² to find 25².
25. 25.Use (a + b)(a − b) = a² − b² to find 97 × 83.
26. 26.Use (a − b)² = a² − 2ab + b² to find 21².
27. 27.If a + b = 4 and ab = 3, what is a² + b²?
28. 28.If a − b = 2 and ab = 24, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 59².
30. 30.Use (a + b)² = a² + 2ab + b² to find 103².
31. 31.Use (a + b)(a − b) = a² − b² to find 81 × 79.
32. 32.Use (a − b)² = a² − 2ab + b² to find 68².
33. 33.Find the value of x² − y² when x = 8 and y = 6.
34. 34.Use (a − b)² = a² − 2ab + b² to find 31².
35. 35.Use (a + b)(a − b) = a² − b² to find 46 × 34.
36. 36.If a − b = 7 and ab = 44, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 2.
38. 38.Find the value of x² − y² when x = 10 and y = 9.
39. 39.If a + b = 7 and ab = 6, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 5 and y = 2.

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