Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 208 · 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 54² − 22².
2. 2.Use (a − b)² = a² − 2ab + b² to find 61².
3. 3.Use (a + b)² = a² + 2ab + b² to find 83².
4. 4.Use (a − b)² = a² − 2ab + b² to find 92².
5. 5.Find the value of x² − 2xy + y² when x = 5 and y = 2.
6. 6.Use (a + b)(a − b) = a² − b² to find 55 × 45.
7. 7.If a − b = 2 and ab = 8, what is a² + b²?
8. 8.If a + b = 5 and ab = 6, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 13².
10. 10.Use (a + b)² = a² + 2ab + b² to find 56².
11. 11.If a + b = 3 and ab = 2, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 42².
13. 13.Use (a + b)(a − b) = a² − b² to find 24 × 16.
14. 14.Use a² − b² = (a + b)(a − b) to find 96² − 70².
15. 15.Use (a + b)² = a² + 2ab + b² to find 34².
16. 16.Use (a + b)² = a² + 2ab + b² to find 31².
17. 17.Use (a − b)² = a² − 2ab + b² to find 17².
18. 18.Use a² − b² = (a + b)(a − b) to find 65² − 9².
19. 19.Use (a + b)(a − b) = a² − b² to find 23 × 17.
20. 20.Use (a + b)(a − b) = a² − b² to find 77 × 63.
21. 21.Use a² − b² = (a + b)(a − b) to find 81² − 18².
22. 22.Use (a − b)² = a² − 2ab + b² to find 12².
23. 23.If a + b = 9 and ab = 18, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 95².
25. 25.Use (a + b)² = a² + 2ab + b² to find 43².
26. 26.Use (a + b)(a − b) = a² − b² to find 93 × 87.
27. 27.Use (a − b)² = a² − 2ab + b² to find 43².
28. 28.Find the value of x² + 2xy + y² when x = 6 and y = 5.
29. 29.Use a² − b² = (a + b)(a − b) to find 99² − 3².
30. 30.Use (a + b)² = a² + 2ab + b² to find 68².
31. 31.Use (a + b)(a − b) = a² − b² to find 43 × 37.
32. 32.Find the value of x² + 2xy + y² when x = 14 and y = 13.
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.Use a² − b² = (a + b)(a − b) to find 80² − 1².
35. 35.Use (a + b)(a − b) = a² − b² to find 54 × 46.
36. 36.Use (a − b)² = a² − 2ab + b² to find 38².
37. 37.Use (a − b)² = a² − 2ab + b² to find 29².
38. 38.Use (a − b)² = a² − 2ab + b² to find 68².
39. 39.Use (a + b)² = a² + 2ab + b² to find 102².
40. 40.If a + b = 9 and ab = 20, what is a² + b²?

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