Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 808 · 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 = 5 and ab = 6, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 57².
3. 3.Use (a + b)² = a² + 2ab + b² to find 52².
4. 4.Use (a + b)(a − b) = a² − b² to find 41 × 39.
5. 5.Use (a + b)(a − b) = a² − b² to find 23 × 17.
6. 6.Use (a + b)(a − b) = a² − b² to find 98 × 82.
7. 7.If a + b = 22 and ab = 120, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 37² − 15².
9. 9.Use (a − b)² = a² − 2ab + b² to find 49².
10. 10.If a − b = 2 and ab = 3, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 11².
12. 12.Use a² − b² = (a + b)(a − b) to find 33² − 3².
13. 13.Use a² − b² = (a + b)(a − b) to find 50² − 21².
14. 14.Find the value of x² − 2xy + y² when x = 13 and y = 11.
15. 15.Find the value of x² − 2xy + y² when x = 15 and y = 7.
16. 16.Use (a − b)² = a² − 2ab + b² to find 34².
17. 17.Use a² − b² = (a + b)(a − b) to find 76² − 22².
18. 18.Use (a + b)² = a² + 2ab + b² to find 94².
19. 19.Use (a + b)(a − b) = a² − b² to find 82 × 78.
20. 20.If a − b = 5 and ab = 36, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 33 × 27.
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 68².
24. 24.Use (a + b)² = a² + 2ab + b² to find 51².
25. 25.Use (a + b)² = a² + 2ab + b² to find 24².
26. 26.Use (a − b)² = a² − 2ab + b² to find 83².
27. 27.Use a² − b² = (a + b)(a − b) to find 21² − 12².
28. 28.Use (a + b)² = a² + 2ab + b² to find 95².
29. 29.Use (a − b)² = a² − 2ab + b² to find 72².
30. 30.Use (a − b)² = a² − 2ab + b² to find 67².
31. 31.Find the value of x² − y² when x = 4 and y = 3.
32. 32.Use (a + b)² = a² + 2ab + b² to find 107².
33. 33.Use (a + b)² = a² + 2ab + b² to find 22².
34. 34.Use (a + b)² = a² + 2ab + b² to find 21².
35. 35.Use (a + b)² = a² + 2ab + b² to find 23².
36. 36.Use (a + b)(a − b) = a² − b² to find 72 × 68.
37. 37.If a − b = 3 and ab = 10, what is a² + b²?
38. 38.Find the value of x² − y² when x = 6 and y = 3.
39. 39.Use (a + b)(a − b) = a² − b² to find 109 × 91.
40. 40.If a − b = 8 and ab = 33, what is a² + b²?

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