Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 16 · 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 67².
2. 2.Use (a + b)(a − b) = a² − b² to find 72 × 68.
3. 3.Use a² − b² = (a + b)(a − b) to find 29² − 11².
4. 4.Use a² − b² = (a + b)(a − b) to find 62² − 20².
5. 5.If a − b = 2 and ab = 8, what is a² + b²?
6. 6.Find the value of x² + 2xy + y² when x = 9 and y = 4.
7. 7.Use (a + b)² = a² + 2ab + b² to find 81².
8. 8.Use (a − b)² = a² − 2ab + b² to find 72².
9. 9.If a − b = 4 and ab = 32, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 80² − 53².
11. 11.If a − b = 5 and ab = 14, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 79².
13. 13.Use a² − b² = (a + b)(a − b) to find 80² − 12².
14. 14.Use (a + b)² = a² + 2ab + b² to find 61².
15. 15.Use a² − b² = (a + b)(a − b) to find 59² − 56².
16. 16.Use (a + b)² = a² + 2ab + b² to find 33².
17. 17.Use (a − b)² = a² − 2ab + b² to find 49².
18. 18.Use (a − b)² = a² − 2ab + b² to find 55².
19. 19.If a − b = 2 and ab = 63, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 22².
21. 21.If a + b = 15 and ab = 44, what is a² + b²?
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 45 × 35.
24. 24.If a + b = 14 and ab = 40, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 11².
26. 26.Use (a + b)² = a² + 2ab + b² to find 38².
27. 27.Use (a − b)² = a² − 2ab + b² to find 81².
28. 28.Use (a − b)² = a² − 2ab + b² to find 58².
29. 29.Use (a + b)(a − b) = a² − b² to find 26 × 14.
30. 30.Use (a + b)(a − b) = a² − b² to find 77 × 63.
31. 31.Use (a + b)² = a² + 2ab + b² to find 75².
32. 32.Use (a + b)² = a² + 2ab + b² to find 59².
33. 33.Use (a + b)(a − b) = a² − b² to find 27 × 13.
34. 34.Find the value of x² + 2xy + y² when x = 11 and y = 1.
35. 35.Use (a + b)(a − b) = a² − b² to find 85 × 75.
36. 36.Use (a + b)² = a² + 2ab + b² to find 16².
37. 37.Use a² − b² = (a + b)(a − b) to find 67² − 43².
38. 38.If a + b = 9 and ab = 18, what is a² + b²?
39. 39.If a − b = 6 and ab = 55, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 12².

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