Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 146 · 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.If a − b = 1 and ab = 30, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 22 × 18.
3. 3.Use (a + b)² = a² + 2ab + b² to find 47².
4. 4.Use (a + b)(a − b) = a² − b² to find 99 × 81.
5. 5.Use (a + b)(a − b) = a² − b² to find 34 × 26.
6. 6.If a − b = 5 and ab = 14, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 82² − 34².
8. 8.Use (a + b)² = a² + 2ab + b² to find 11².
9. 9.Find the value of x² − 2xy + y² when x = 7 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 11².
11. 11.Use a² − b² = (a + b)(a − b) to find 77² − 36².
12. 12.Use (a + b)(a − b) = a² − b² to find 49 × 31.
13. 13.Use (a + b)² = a² + 2ab + b² to find 71².
14. 14.Use a² − b² = (a + b)(a − b) to find 58² − 4².
15. 15.Use (a − b)² = a² − 2ab + b² to find 91².
16. 16.Use (a − b)² = a² − 2ab + b² to find 26².
17. 17.Use (a − b)² = a² − 2ab + b² to find 18².
18. 18.Find the value of x² − 2xy + y² when x = 8 and y = 3.
19. 19.Use (a − b)² = a² − 2ab + b² to find 28².
20. 20.Use (a − b)² = a² − 2ab + b² to find 94².
21. 21.Use a² − b² = (a + b)(a − b) to find 30² − 6².
22. 22.Use (a − b)² = a² − 2ab + b² to find 38².
23. 23.Use (a − b)² = a² − 2ab + b² to find 54².
24. 24.Find the value of x² + 2xy + y² when x = 12 and y = 3.
25. 25.Find the value of x² − y² when x = 5 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 61².
27. 27.Use (a + b)(a − b) = a² − b² to find 79 × 61.
28. 28.Use (a − b)² = a² − 2ab + b² to find 48².
29. 29.Use (a − b)² = a² − 2ab + b² to find 21².
30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 2.
31. 31.Use a² − b² = (a + b)(a − b) to find 65² − 10².
32. 32.Use a² − b² = (a + b)(a − b) to find 44² − 18².
33. 33.Use (a + b)² = a² + 2ab + b² to find 95².
34. 34.Use (a + b)² = a² + 2ab + b² to find 96².
35. 35.Use a² − b² = (a + b)(a − b) to find 81² − 13².
36. 36.Use a² − b² = (a + b)(a − b) to find 80² − 21².
37. 37.Use (a + b)(a − b) = a² − b² to find 28 × 12.
38. 38.If a − b = 5 and ab = 6, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 8 and y = 4.
40. 40.Use a² − b² = (a + b)(a − b) to find 34² − 9².

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