Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 87 · 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 = 4 and y = 1.
2. 2.Find the value of x² − y² when x = 15 and y = 11.
3. 3.Use (a + b)(a − b) = a² − b² to find 29 × 11.
4. 4.Find the value of x² + 2xy + y² when x = 12 and y = 1.
5. 5.Use a² − b² = (a + b)(a − b) to find 41² − 1².
6. 6.Use (a + b)² = a² + 2ab + b² to find 94².
7. 7.Use (a + b)² = a² + 2ab + b² to find 19².
8. 8.Use (a − b)² = a² − 2ab + b² to find 35².
9. 9.Use (a + b)² = a² + 2ab + b² to find 86².
10. 10.Use (a − b)² = a² − 2ab + b² to find 82².
11. 11.If a − b = 3 and ab = 54, what is a² + b²?
12. 12.If a + b = 14 and ab = 40, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 41² − 36².
14. 14.Use (a − b)² = a² − 2ab + b² to find 16².
15. 15.Use a² − b² = (a + b)(a − b) to find 81² − 5².
16. 16.Use (a − b)² = a² − 2ab + b² to find 19².
17. 17.If a + b = 11 and ab = 18, what is a² + b²?
18. 18.Find the value of x² + 2xy + y² when x = 8 and y = 2.
19. 19.Use (a + b)² = a² + 2ab + b² to find 38².
20. 20.Use (a + b)(a − b) = a² − b² to find 39 × 21.
21. 21.Use (a − b)² = a² − 2ab + b² to find 12².
22. 22.Use a² − b² = (a + b)(a − b) to find 49² − 10².
23. 23.Use a² − b² = (a + b)(a − b) to find 73² − 72².
24. 24.Use (a + b)² = a² + 2ab + b² to find 67².
25. 25.Use (a + b)(a − b) = a² − b² to find 85 × 75.
26. 26.If a + b = 8 and ab = 12, what is a² + b²?
27. 27.If a − b = 7 and ab = 8, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 28².
29. 29.Use (a − b)² = a² − 2ab + b² to find 54².
30. 30.Find the value of x² + 2xy + y² when x = 10 and y = 9.
31. 31.Find the value of x² − 2xy + y² when x = 5 and y = 2.
32. 32.If a − b = 5 and ab = 36, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 39² − 23².
34. 34.Use (a + b)² = a² + 2ab + b² to find 12².
35. 35.If a + b = 19 and ab = 90, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 40² − 32².
37. 37.Use a² − b² = (a + b)(a − b) to find 64² − 28².
38. 38.If a − b = 2 and ab = 3, what is a² + b²?
39. 39.Find the value of x² − y² when x = 4 and y = 2.
40. 40.Use (a + b)(a − b) = a² − b² to find 36 × 24.

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