Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 521 · 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 a² − b² = (a + b)(a − b) to find 91² − 22².
2. 2.Use (a − b)² = a² − 2ab + b² to find 24².
3. 3.Use (a − b)² = a² − 2ab + b² to find 73².
4. 4.Use (a + b)² = a² + 2ab + b² to find 19².
5. 5.Use (a − b)² = a² − 2ab + b² to find 62².
6. 6.Use a² − b² = (a + b)(a − b) to find 56² − 12².
7. 7.Use (a − b)² = a² − 2ab + b² to find 17².
8. 8.If a − b = 4 and ab = 21, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 71².
10. 10.If a + b = 4 and ab = 3, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 102².
12. 12.Use (a + b)² = a² + 2ab + b² to find 85².
13. 13.Find the value of x² − 2xy + y² when x = 14 and y = 3.
14. 14.Use (a + b)² = a² + 2ab + b² to find 18².
15. 15.If a + b = 9 and ab = 20, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 13².
17. 17.Use (a + b)² = a² + 2ab + b² to find 57².
18. 18.If a + b = 12 and ab = 35, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 70² − 17².
20. 20.If a + b = 7 and ab = 10, what is a² + b²?
21. 21.If a − b = 3 and ab = 70, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 6.
23. 23.Use (a + b)² = a² + 2ab + b² to find 74².
24. 24.Use (a − b)² = a² − 2ab + b² to find 34².
25. 25.Use (a + b)² = a² + 2ab + b² to find 15².
26. 26.If a + b = 21 and ab = 110, what is a² + b²?
27. 27.If a − b = 5 and ab = 14, what is a² + b²?
28. 28.If a + b = 5 and ab = 4, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 36².
30. 30.Use (a + b)(a − b) = a² − b² to find 42 × 38.
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 8.
32. 32.If a − b = 1 and ab = 2, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 9 and y = 1.
34. 34.Use (a + b)² = a² + 2ab + b² to find 22².
35. 35.Find the value of x² − 2xy + y² when x = 3 and y = 1.
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.Use (a + b)² = a² + 2ab + b² to find 52².
38. 38.Find the value of x² − y² when x = 10 and y = 5.
39. 39.If a − b = 4 and ab = 45, what is a² + b²?
40. 40.If a + b = 13 and ab = 12, what is a² + b²?

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