Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 134 · 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 = 23 and ab = 132, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 56².
3. 3.Use (a + b)(a − b) = a² − b² to find 78 × 62.
4. 4.Use (a + b)² = a² + 2ab + b² to find 65².
5. 5.Use (a − b)² = a² − 2ab + b² to find 99².
6. 6.Use (a + b)² = a² + 2ab + b² to find 13².
7. 7.Use (a + b)(a − b) = a² − b² to find 89 × 71.
8. 8.Use a² − b² = (a + b)(a − b) to find 83² − 29².
9. 9.Use (a − b)² = a² − 2ab + b² to find 11².
10. 10.Use (a + b)² = a² + 2ab + b² to find 96².
11. 11.Use (a + b)² = a² + 2ab + b² to find 25².
12. 12.Use (a − b)² = a² − 2ab + b² to find 91².
13. 13.Use (a + b)² = a² + 2ab + b² to find 11².
14. 14.If a + b = 9 and ab = 14, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 61².
16. 16.Use a² − b² = (a + b)(a − b) to find 64² − 44².
17. 17.Use (a − b)² = a² − 2ab + b² to find 55².
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 4.
19. 19.If a − b = 7 and ab = 60, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 52².
21. 21.Use (a − b)² = a² − 2ab + b² to find 94².
22. 22.If a + b = 14 and ab = 45, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 28 × 12.
24. 24.Use (a − b)² = a² − 2ab + b² to find 97².
25. 25.Use (a + b)² = a² + 2ab + b² to find 75².
26. 26.Find the value of x² − y² when x = 15 and y = 11.
27. 27.Use (a − b)² = a² − 2ab + b² to find 96².
28. 28.If a − b = 3 and ab = 10, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 92².
30. 30.Use (a + b)(a − b) = a² − b² to find 103 × 97.
31. 31.Find the value of x² − y² when x = 12 and y = 7.
32. 32.Use (a + b)² = a² + 2ab + b² to find 69².
33. 33.Use a² − b² = (a + b)(a − b) to find 77² − 62².
34. 34.Use (a − b)² = a² − 2ab + b² to find 49².
35. 35.Use (a + b)(a − b) = a² − b² to find 77 × 63.
36. 36.Use (a + b)² = a² + 2ab + b² to find 46².
37. 37.If a + b = 9 and ab = 20, what is a² + b²?
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 43 × 37.
40. 40.Use a² − b² = (a + b)(a − b) to find 58² − 2².

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