Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 905 · 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 89².
2. 2.Use a² − b² = (a + b)(a − b) to find 31² − 8².
3. 3.Use (a + b)² = a² + 2ab + b² to find 104².
4. 4.Use (a + b)² = a² + 2ab + b² to find 42².
5. 5.Use a² − b² = (a + b)(a − b) to find 80² − 23².
6. 6.Find the value of x² + 2xy + y² when x = 8 and y = 3.
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 10 and y = 1.
9. 9.Use a² − b² = (a + b)(a − b) to find 80² − 35².
10. 10.Use (a − b)² = a² − 2ab + b² to find 39².
11. 11.Use (a + b)(a − b) = a² − b² to find 78 × 62.
12. 12.Use (a + b)² = a² + 2ab + b² to find 63².
13. 13.Use (a + b)² = a² + 2ab + b² to find 88².
14. 14.Find the value of x² − 2xy + y² when x = 3 and y = 2.
15. 15.Use (a + b)² = a² + 2ab + b² to find 102².
16. 16.Use (a + b)(a − b) = a² − b² to find 109 × 91.
17. 17.If a + b = 8 and ab = 12, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 14².
19. 19.Use (a + b)² = a² + 2ab + b² to find 72².
20. 20.Use (a − b)² = a² − 2ab + b² to find 82².
21. 21.Use (a + b)² = a² + 2ab + b² to find 57².
22. 22.Use (a − b)² = a² − 2ab + b² to find 45².
23. 23.Use a² − b² = (a + b)(a − b) to find 61² − 31².
24. 24.Use (a + b)(a − b) = a² − b² to find 28 × 12.
25. 25.Find the value of x² − 2xy + y² when x = 13 and y = 10.
26. 26.Use (a + b)(a − b) = a² − b² to find 43 × 37.
27. 27.Use a² − b² = (a + b)(a − b) to find 31² − 25².
28. 28.Use (a + b)² = a² + 2ab + b² to find 23².
29. 29.Use a² − b² = (a + b)(a − b) to find 50² − 19².
30. 30.Find the value of x² − y² when x = 8 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 79².
32. 32.Use (a + b)(a − b) = a² − b² to find 24 × 16.
33. 33.Use (a + b)² = a² + 2ab + b² to find 82².
34. 34.Use (a − b)² = a² − 2ab + b² to find 95².
35. 35.Find the value of x² + 2xy + y² when x = 6 and y = 3.
36. 36.Use a² − b² = (a + b)(a − b) to find 64² − 30².
37. 37.Use (a + b)(a − b) = a² − b² to find 66 × 54.
38. 38.Use (a − b)² = a² − 2ab + b² to find 68².
39. 39.Use (a + b)² = a² + 2ab + b² to find 36².
40. 40.Use a² − b² = (a + b)(a − b) to find 49² − 18².

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