Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 138 · 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 24².
2. 2.Use (a + b)² = a² + 2ab + b² to find 53².
3. 3.If a − b = 2 and ab = 80, what is a² + b²?
4. 4.If a − b = 6 and ab = 7, what is a² + b²?
5. 5.If a + b = 7 and ab = 10, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 59² − 27².
7. 7.Find the value of x² + 2xy + y² when x = 15 and y = 8.
8. 8.Use (a − b)² = a² − 2ab + b² to find 35².
9. 9.Find the value of x² − 2xy + y² when x = 13 and y = 6.
10. 10.Use (a + b)(a − b) = a² − b² to find 33 × 27.
11. 11.Use (a + b)² = a² + 2ab + b² to find 74².
12. 12.Use (a − b)² = a² − 2ab + b² to find 81².
13. 13.If a − b = 5 and ab = 14, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 51².
15. 15.Find the value of x² − 2xy + y² when x = 9 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 65² − 25².
17. 17.Use a² − b² = (a + b)(a − b) to find 40² − 25².
18. 18.Use (a + b)² = a² + 2ab + b² to find 105².
19. 19.Find the value of x² − 2xy + y² when x = 14 and y = 1.
20. 20.Use (a − b)² = a² − 2ab + b² to find 66².
21. 21.If a + b = 4 and ab = 3, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 21².
23. 23.Find the value of x² − y² when x = 5 and y = 3.
24. 24.Use (a + b)² = a² + 2ab + b² to find 96².
25. 25.Use (a + b)² = a² + 2ab + b² to find 91².
26. 26.Use (a + b)² = a² + 2ab + b² to find 34².
27. 27.Use (a + b)(a − b) = a² − b² to find 59 × 41.
28. 28.Use (a − b)² = a² − 2ab + b² to find 54².
29. 29.Find the value of x² − y² when x = 3 and y = 2.
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 68² − 32².
32. 32.Use a² − b² = (a + b)(a − b) to find 45² − 9².
33. 33.Use a² − b² = (a + b)(a − b) to find 45² − 21².
34. 34.Use (a + b)² = a² + 2ab + b² to find 27².
35. 35.Use (a + b)² = a² + 2ab + b² to find 52².
36. 36.If a + b = 8 and ab = 12, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 47².
38. 38.Use a² − b² = (a + b)(a − b) to find 51² − 18².
39. 39.Use (a − b)² = a² − 2ab + b² to find 47².
40. 40.Use a² − b² = (a + b)(a − b) to find 46² − 15².

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