Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 428 · 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 = 7 and ab = 8, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 99².
3. 3.Find the value of x² + 2xy + y² when x = 7 and y = 2.
4. 4.Find the value of x² − y² when x = 11 and y = 1.
5. 5.Use (a + b)(a − b) = a² − b² to find 83 × 77.
6. 6.Use (a + b)(a − b) = a² − b² to find 77 × 63.
7. 7.Use (a − b)² = a² − 2ab + b² to find 91².
8. 8.Use (a − b)² = a² − 2ab + b² to find 51².
9. 9.Find the value of x² + 2xy + y² when x = 4 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 11².
11. 11.Use (a + b)² = a² + 2ab + b² to find 36².
12. 12.Find the value of x² − y² when x = 9 and y = 4.
13. 13.Use (a + b)(a − b) = a² − b² to find 43 × 37.
14. 14.Find the value of x² − 2xy + y² when x = 8 and y = 2.
15. 15.Use (a − b)² = a² − 2ab + b² to find 59².
16. 16.Use (a − b)² = a² − 2ab + b² to find 45².
17. 17.Use (a + b)² = a² + 2ab + b² to find 95².
18. 18.Use (a − b)² = a² − 2ab + b² to find 38².
19. 19.Use a² − b² = (a + b)(a − b) to find 62² − 6².
20. 20.Use (a + b)(a − b) = a² − b² to find 38 × 22.
21. 21.Use a² − b² = (a + b)(a − b) to find 33² − 28².
22. 22.Find the value of x² + 2xy + y² when x = 5 and y = 2.
23. 23.Use (a + b)(a − b) = a² − b² to find 99 × 81.
24. 24.Find the value of x² − y² when x = 7 and y = 1.
25. 25.If a + b = 6 and ab = 5, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 108 × 92.
27. 27.If a − b = 7 and ab = 18, what is a² + b²?
28. 28.Find the value of x² − 2xy + y² when x = 3 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 52².
30. 30.Use (a − b)² = a² − 2ab + b² to find 96².
31. 31.Use (a + b)² = a² + 2ab + b² to find 42².
32. 32.Use (a − b)² = a² − 2ab + b² to find 77².
33. 33.If a + b = 8 and ab = 15, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 41² − 18².
35. 35.Use (a + b)² = a² + 2ab + b² to find 71².
36. 36.Use (a + b)² = a² + 2ab + b² to find 27².
37. 37.Use (a + b)(a − b) = a² − b² to find 33 × 27.
38. 38.Use (a + b)² = a² + 2ab + b² to find 12².
39. 39.Use a² − b² = (a + b)(a − b) to find 94² − 14².
40. 40.Use (a + b)(a − b) = a² − b² to find 71 × 69.

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