Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 671 · 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 − 2xy + y² when x = 5 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 21² − 6².
3. 3.If a + b = 11 and ab = 24, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 83².
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 3.
6. 6.Use (a + b)(a − b) = a² − b² to find 33 × 27.
7. 7.If a + b = 9 and ab = 18, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 30² − 4².
9. 9.Use (a + b)² = a² + 2ab + b² to find 77².
10. 10.Use (a + b)² = a² + 2ab + b² to find 13².
11. 11.Use (a + b)² = a² + 2ab + b² to find 82².
12. 12.Find the value of x² − 2xy + y² when x = 13 and y = 1.
13. 13.Use (a + b)(a − b) = a² − b² to find 29 × 11.
14. 14.Use (a + b)(a − b) = a² − b² to find 21 × 19.
15. 15.Use a² − b² = (a + b)(a − b) to find 75² − 25².
16. 16.Find the value of x² − y² when x = 13 and y = 7.
17. 17.Use a² − b² = (a + b)(a − b) to find 86² − 57².
18. 18.Use (a − b)² = a² − 2ab + b² to find 31².
19. 19.If a + b = 5 and ab = 6, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 27 × 13.
21. 21.Use (a + b)² = a² + 2ab + b² to find 76².
22. 22.If a − b = 7 and ab = 30, what is a² + b²?
23. 23.Find the value of x² + 2xy + y² when x = 8 and y = 6.
24. 24.Use (a + b)² = a² + 2ab + b² to find 47².
25. 25.Use a² − b² = (a + b)(a − b) to find 23² − 19².
26. 26.Use a² − b² = (a + b)(a − b) to find 77² − 27².
27. 27.Use a² − b² = (a + b)(a − b) to find 50² − 44².
28. 28.Find the value of x² − y² when x = 13 and y = 6.
29. 29.Use (a + b)² = a² + 2ab + b² to find 65².
30. 30.Find the value of x² − y² when x = 6 and y = 3.
31. 31.Use (a − b)² = a² − 2ab + b² to find 28².
32. 32.Use (a − b)² = a² − 2ab + b² to find 94².
33. 33.Use a² − b² = (a + b)(a − b) to find 97² − 41².
34. 34.Use a² − b² = (a + b)(a − b) to find 63² − 58².
35. 35.Use (a − b)² = a² − 2ab + b² to find 36².
36. 36.Use a² − b² = (a + b)(a − b) to find 91² − 14².
37. 37.Use (a − b)² = a² − 2ab + b² to find 19².
38. 38.Use a² − b² = (a + b)(a − b) to find 34² − 27².
39. 39.Use (a + b)(a − b) = a² − b² to find 59 × 41.
40. 40.Use (a + b)(a − b) = a² − b² to find 31 × 29.

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