Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 929 · 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.Find the value of x² − y² when x = 4 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 28².
3. 3.If a + b = 8 and ab = 12, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 38².
5. 5.Use (a + b)(a − b) = a² − b² to find 91 × 89.
6. 6.Use (a + b)(a − b) = a² − b² to find 34 × 26.
7. 7.If a + b = 6 and ab = 5, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 6 and y = 1.
9. 9.Find the value of x² − y² when x = 5 and y = 4.
10. 10.Use a² − b² = (a + b)(a − b) to find 63² − 58².
11. 11.Use (a − b)² = a² − 2ab + b² to find 55².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.If a + b = 14 and ab = 33, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 18².
15. 15.Use (a + b)(a − b) = a² − b² to find 54 × 46.
16. 16.If a + b = 10 and ab = 24, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 75².
18. 18.If a + b = 9 and ab = 14, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 79².
20. 20.Use (a − b)² = a² − 2ab + b² to find 59².
21. 21.Use (a + b)² = a² + 2ab + b² to find 24².
22. 22.Use (a + b)² = a² + 2ab + b² to find 76².
23. 23.Use (a + b)(a − b) = a² − b² to find 35 × 25.
24. 24.Find the value of x² − y² when x = 3 and y = 2.
25. 25.Use (a + b)(a − b) = a² − b² to find 43 × 37.
26. 26.Use (a + b)² = a² + 2ab + b² to find 81².
27. 27.Use a² − b² = (a + b)(a − b) to find 62² − 59².
28. 28.Use (a + b)² = a² + 2ab + b² to find 91².
29. 29.Use (a + b)² = a² + 2ab + b² to find 71².
30. 30.Use (a + b)² = a² + 2ab + b² to find 21².
31. 31.Use (a − b)² = a² − 2ab + b² to find 29².
32. 32.Use a² − b² = (a + b)(a − b) to find 40² − 6².
33. 33.If a − b = 5 and ab = 24, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 94².
35. 35.Use a² − b² = (a + b)(a − b) to find 63² − 32².
36. 36.Find the value of x² − 2xy + y² when x = 6 and y = 2.
37. 37.Find the value of x² + 2xy + y² when x = 5 and y = 2.
38. 38.Use (a + b)² = a² + 2ab + b² to find 51².
39. 39.Use a² − b² = (a + b)(a − b) to find 27² − 22².
40. 40.If a − b = 5 and ab = 6, what is a² + b²?

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