Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 520 · 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 = 2.
2. 2.Find the value of x² + 2xy + y² when x = 15 and y = 10.
3. 3.Use (a − b)² = a² − 2ab + b² to find 15².
4. 4.Find the value of x² − 2xy + y² when x = 11 and y = 8.
5. 5.Use (a + b)² = a² + 2ab + b² to find 89².
6. 6.Use (a + b)(a − b) = a² − b² to find 27 × 13.
7. 7.Find the value of x² − y² when x = 5 and y = 4.
8. 8.Use a² − b² = (a + b)(a − b) to find 78² − 35².
9. 9.Find the value of x² − y² when x = 14 and y = 3.
10. 10.Use (a + b)² = a² + 2ab + b² to find 27².
11. 11.Use (a + b)² = a² + 2ab + b² to find 34².
12. 12.Use (a − b)² = a² − 2ab + b² to find 28².
13. 13.Use (a + b)(a − b) = a² − b² to find 46 × 34.
14. 14.Use (a − b)² = a² − 2ab + b² to find 89².
15. 15.Find the value of x² − y² when x = 11 and y = 10.
16. 16.Use (a − b)² = a² − 2ab + b² to find 22².
17. 17.Use (a − b)² = a² − 2ab + b² to find 33².
18. 18.If a − b = 1 and ab = 2, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 8 and y = 2.
20. 20.Use (a − b)² = a² − 2ab + b² to find 94².
21. 21.If a − b = 2 and ab = 15, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 25².
23. 23.Use (a + b)² = a² + 2ab + b² to find 55².
24. 24.Use (a + b)² = a² + 2ab + b² to find 93².
25. 25.Use (a − b)² = a² − 2ab + b² to find 76².
26. 26.Use a² − b² = (a + b)(a − b) to find 89² − 1².
27. 27.Use (a + b)(a − b) = a² − b² to find 49 × 31.
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 51 × 49.
30. 30.Use (a + b)(a − b) = a² − b² to find 31 × 29.
31. 31.Use (a + b)² = a² + 2ab + b² to find 85².
32. 32.Use (a + b)² = a² + 2ab + b² to find 83².
33. 33.Use (a − b)² = a² − 2ab + b² to find 48².
34. 34.Use (a + b)² = a² + 2ab + b² to find 13².
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 1.
36. 36.If a + b = 6 and ab = 8, what is a² + b²?
37. 37.Find the value of x² − y² when x = 10 and y = 3.
38. 38.If a + b = 6 and ab = 5, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 94².
40. 40.Use (a + b)(a − b) = a² − b² to find 69 × 51.

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