Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 658 · 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 = 3.
2. 2.Find the value of x² − y² when x = 5 and y = 4.
3. 3.Use (a − b)² = a² − 2ab + b² to find 31².
4. 4.Use a² − b² = (a + b)(a − b) to find 88² − 33².
5. 5.Use (a + b)² = a² + 2ab + b² to find 33².
6. 6.Find the value of x² − y² when x = 4 and y = 3.
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 3.
8. 8.Use (a + b)(a − b) = a² − b² to find 85 × 75.
9. 9.Use (a + b)² = a² + 2ab + b² to find 101².
10. 10.Find the value of x² + 2xy + y² when x = 8 and y = 3.
11. 11.Use (a + b)(a − b) = a² − b² to find 49 × 31.
12. 12.Use (a − b)² = a² − 2ab + b² to find 66².
13. 13.Use (a + b)(a − b) = a² − b² to find 72 × 68.
14. 14.Use (a − b)² = a² − 2ab + b² to find 87².
15. 15.Use (a − b)² = a² − 2ab + b² to find 21².
16. 16.Use (a + b)² = a² + 2ab + b² to find 82².
17. 17.Use (a + b)(a − b) = a² − b² to find 39 × 21.
18. 18.If a − b = 3 and ab = 40, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 77².
20. 20.Find the value of x² − y² when x = 7 and y = 4.
21. 21.Use a² − b² = (a + b)(a − b) to find 41² − 2².
22. 22.If a − b = 1 and ab = 42, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 61².
24. 24.Use (a + b)(a − b) = a² − b² to find 54 × 46.
25. 25.Use (a + b)² = a² + 2ab + b² to find 35².
26. 26.Use (a + b)(a − b) = a² − b² to find 104 × 96.
27. 27.If a + b = 4 and ab = 3, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 22 × 18.
29. 29.Use (a − b)² = a² − 2ab + b² to find 88².
30. 30.If a + b = 9 and ab = 8, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 28².
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 8.
33. 33.Use (a − b)² = a² − 2ab + b² to find 86².
34. 34.Use (a − b)² = a² − 2ab + b² to find 11².
35. 35.Use (a + b)(a − b) = a² − b² to find 67 × 53.
36. 36.If a + b = 11 and ab = 18, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 29².
39. 39.Use (a − b)² = a² − 2ab + b² to find 96².
40. 40.Find the value of x² − 2xy + y² when x = 7 and y = 3.

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