Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 586 · 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 (a + b)² = a² + 2ab + b² to find 82².
2. 2.Use a² − b² = (a + b)(a − b) to find 73² − 26².
3. 3.If a + b = 5 and ab = 4, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 72².
5. 5.Use (a − b)² = a² − 2ab + b² to find 17².
6. 6.Find the value of x² + 2xy + y² when x = 9 and y = 5.
7. 7.Use a² − b² = (a + b)(a − b) to find 39² − 13².
8. 8.Find the value of x² − 2xy + y² when x = 15 and y = 8.
9. 9.Use a² − b² = (a + b)(a − b) to find 74² − 31².
10. 10.Use (a + b)(a − b) = a² − b² to find 73 × 67.
11. 11.Find the value of x² − y² when x = 4 and y = 1.
12. 12.If a + b = 6 and ab = 5, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 41 × 39.
14. 14.Use (a + b)² = a² + 2ab + b² to find 71².
15. 15.Find the value of x² + 2xy + y² when x = 12 and y = 10.
16. 16.If a + b = 4 and ab = 3, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 8 and y = 4.
18. 18.Use (a − b)² = a² − 2ab + b² to find 79².
19. 19.Use (a + b)(a − b) = a² − b² to find 27 × 13.
20. 20.Use (a − b)² = a² − 2ab + b² to find 22².
21. 21.Find the value of x² + 2xy + y² when x = 4 and y = 1.
22. 22.Use (a + b)(a − b) = a² − b² to find 63 × 57.
23. 23.Use (a + b)(a − b) = a² − b² to find 57 × 43.
24. 24.Use (a + b)² = a² + 2ab + b² to find 38².
25. 25.If a + b = 6 and ab = 8, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 93 × 87.
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 4.
28. 28.Use (a + b)(a − b) = a² − b² to find 26 × 14.
29. 29.Use (a − b)² = a² − 2ab + b² to find 48².
30. 30.Find the value of x² − y² when x = 10 and y = 2.
31. 31.Find the value of x² − y² when x = 14 and y = 11.
32. 32.Use (a + b)² = a² + 2ab + b² to find 108².
33. 33.Use (a + b)(a − b) = a² − b² to find 82 × 78.
34. 34.Use (a − b)² = a² − 2ab + b² to find 83².
35. 35.If a + b = 8 and ab = 15, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 68² − 39².
37. 37.Use a² − b² = (a + b)(a − b) to find 40² − 36².
38. 38.Use (a + b)(a − b) = a² − b² to find 87 × 73.
39. 39.Find the value of x² + 2xy + y² when x = 14 and y = 6.
40. 40.Use (a − b)² = a² − 2ab + b² to find 58².

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