Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 898 · 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 19².
2. 2.Use (a + b)(a − b) = a² − b² to find 91 × 89.
3. 3.Find the value of x² + 2xy + y² when x = 15 and y = 9.
4. 4.If a + b = 21 and ab = 110, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 11².
6. 6.If a + b = 10 and ab = 9, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 68 × 52.
8. 8.Use a² − b² = (a + b)(a − b) to find 69² − 23².
9. 9.Use a² − b² = (a + b)(a − b) to find 37² − 24².
10. 10.Use (a + b)² = a² + 2ab + b² to find 71².
11. 11.Use (a − b)² = a² − 2ab + b² to find 86².
12. 12.Find the value of x² + 2xy + y² when x = 8 and y = 5.
13. 13.Use (a − b)² = a² − 2ab + b² to find 38².
14. 14.Use a² − b² = (a + b)(a − b) to find 56² − 2².
15. 15.Use a² − b² = (a + b)(a − b) to find 96² − 31².
16. 16.Use a² − b² = (a + b)(a − b) to find 47² − 8².
17. 17.If a + b = 11 and ab = 24, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 66².
19. 19.Use (a + b)² = a² + 2ab + b² to find 54².
20. 20.Use a² − b² = (a + b)(a − b) to find 84² − 3².
21. 21.Use (a + b)² = a² + 2ab + b² to find 36².
22. 22.Use (a − b)² = a² − 2ab + b² to find 26².
23. 23.Use (a + b)² = a² + 2ab + b² to find 74².
24. 24.Use (a + b)(a − b) = a² − b² to find 44 × 36.
25. 25.Use (a + b)(a − b) = a² − b² to find 74 × 66.
26. 26.Use (a − b)² = a² − 2ab + b² to find 67².
27. 27.Use a² − b² = (a + b)(a − b) to find 75² − 44².
28. 28.Find the value of x² − 2xy + y² when x = 9 and y = 6.
29. 29.Use (a + b)² = a² + 2ab + b² to find 28².
30. 30.Use (a − b)² = a² − 2ab + b² to find 76².
31. 31.Use (a + b)² = a² + 2ab + b² to find 69².
32. 32.If a + b = 4 and ab = 3, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 11 and y = 6.
34. 34.Use (a + b)² = a² + 2ab + b² to find 95².
35. 35.Use (a + b)(a − b) = a² − b² to find 34 × 26.
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 5 and y = 3.
38. 38.Use (a + b)² = a² + 2ab + b² to find 72².
39. 39.Use a² − b² = (a + b)(a − b) to find 38² − 15².
40. 40.Find the value of x² − y² when x = 3 and y = 1.

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