Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 35 · 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 = 8 and y = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 87 × 73.
3. 3.Use (a − b)² = a² − 2ab + b² to find 72².
4. 4.Use (a + b)² = a² + 2ab + b² to find 86².
5. 5.Use (a − b)² = a² − 2ab + b² to find 19².
6. 6.Find the value of x² − y² when x = 14 and y = 8.
7. 7.Use (a − b)² = a² − 2ab + b² to find 39².
8. 8.Find the value of x² − 2xy + y² when x = 4 and y = 1.
9. 9.Use (a − b)² = a² − 2ab + b² to find 17².
10. 10.Use a² − b² = (a + b)(a − b) to find 35² − 2².
11. 11.Use a² − b² = (a + b)(a − b) to find 34² − 32².
12. 12.Use (a − b)² = a² − 2ab + b² to find 24².
13. 13.Use (a − b)² = a² − 2ab + b² to find 81².
14. 14.Use (a − b)² = a² − 2ab + b² to find 45².
15. 15.If a + b = 5 and ab = 4, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 70² − 27².
17. 17.Find the value of x² − y² when x = 13 and y = 5.
18. 18.If a + b = 21 and ab = 110, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 82² − 56².
20. 20.If a + b = 9 and ab = 18, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 43 × 37.
22. 22.Use (a + b)(a − b) = a² − b² to find 42 × 38.
23. 23.Use a² − b² = (a + b)(a − b) to find 93² − 63².
24. 24.Use (a − b)² = a² − 2ab + b² to find 88².
25. 25.Find the value of x² − 2xy + y² when x = 13 and y = 5.
26. 26.Find the value of x² + 2xy + y² when x = 7 and y = 2.
27. 27.Use (a − b)² = a² − 2ab + b² to find 74².
28. 28.Use a² − b² = (a + b)(a − b) to find 57² − 47².
29. 29.If a + b = 15 and ab = 54, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 22² − 12².
31. 31.Use (a + b)(a − b) = a² − b² to find 44 × 36.
32. 32.Find the value of x² + 2xy + y² when x = 4 and y = 2.
33. 33.If a − b = 4 and ab = 12, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 49² − 10².
35. 35.Use (a + b)(a − b) = a² − b² to find 47 × 33.
36. 36.Use a² − b² = (a + b)(a − b) to find 99² − 80².
37. 37.Use a² − b² = (a + b)(a − b) to find 96² − 38².
38. 38.Use (a + b)² = a² + 2ab + b² to find 17².
39. 39.If a − b = 1 and ab = 2, what is a² + b²?
40. 40.Find the value of x² − y² when x = 3 and y = 2.

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