Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 882 · 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 27².
2. 2.Use (a − b)² = a² − 2ab + b² to find 64².
3. 3.Use (a + b)² = a² + 2ab + b² to find 32².
4. 4.If a − b = 3 and ab = 10, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 69².
6. 6.If a + b = 3 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 65².
8. 8.Use (a + b)² = a² + 2ab + b² to find 55².
9. 9.Find the value of x² − y² when x = 5 and y = 2.
10. 10.Use (a + b)(a − b) = a² − b² to find 31 × 29.
11. 11.Use (a + b)(a − b) = a² − b² to find 54 × 46.
12. 12.If a + b = 9 and ab = 14, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 17².
14. 14.Find the value of x² − 2xy + y² when x = 14 and y = 4.
15. 15.Use a² − b² = (a + b)(a − b) to find 51² − 18².
16. 16.If a + b = 17 and ab = 60, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 49² − 12².
18. 18.Use (a + b)² = a² + 2ab + b² to find 33².
19. 19.Use (a − b)² = a² − 2ab + b² to find 29².
20. 20.Use a² − b² = (a + b)(a − b) to find 21² − 2².
21. 21.Use (a − b)² = a² − 2ab + b² to find 32².
22. 22.Use (a − b)² = a² − 2ab + b² to find 21².
23. 23.Use (a + b)² = a² + 2ab + b² to find 15².
24. 24.Use (a + b)² = a² + 2ab + b² to find 11².
25. 25.Use (a − b)² = a² − 2ab + b² to find 74².
26. 26.Use a² − b² = (a + b)(a − b) to find 49² − 28².
27. 27.Use (a + b)(a − b) = a² − b² to find 73 × 67.
28. 28.If a − b = 2 and ab = 15, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 6².
30. 30.Use a² − b² = (a + b)(a − b) to find 53² − 45².
31. 31.Use (a + b)² = a² + 2ab + b² to find 44².
32. 32.If a + b = 16 and ab = 63, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 8 and y = 6.
34. 34.Use (a − b)² = a² − 2ab + b² to find 81².
35. 35.Use (a + b)² = a² + 2ab + b² to find 109².
36. 36.Use a² − b² = (a + b)(a − b) to find 77² − 70².
37. 37.Use a² − b² = (a + b)(a − b) to find 51² − 20².
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Use (a − b)² = a² − 2ab + b² to find 42².
40. 40.Use (a + b)(a − b) = a² − b² to find 43 × 37.

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