Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 515 · 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 = 6 and y = 1.
2. 2.Find the value of x² − 2xy + y² when x = 3 and y = 2.
3. 3.Use (a + b)(a − b) = a² − b² to find 72 × 68.
4. 4.Use (a + b)² = a² + 2ab + b² to find 79².
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 3.
6. 6.Use a² − b² = (a + b)(a − b) to find 46² − 17².
7. 7.Use (a + b)² = a² + 2ab + b² to find 76².
8. 8.Use (a + b)² = a² + 2ab + b² to find 69².
9. 9.Use (a + b)(a − b) = a² − b² to find 29 × 11.
10. 10.Use (a + b)(a − b) = a² − b² to find 81 × 79.
11. 11.Use (a + b)² = a² + 2ab + b² to find 68².
12. 12.Use a² − b² = (a + b)(a − b) to find 90² − 85².
13. 13.Use (a + b)² = a² + 2ab + b² to find 95².
14. 14.Find the value of x² − 2xy + y² when x = 7 and y = 6.
15. 15.Find the value of x² − y² when x = 13 and y = 12.
16. 16.Use a² − b² = (a + b)(a − b) to find 56² − 54².
17. 17.Use (a + b)² = a² + 2ab + b² to find 96².
18. 18.Use (a − b)² = a² − 2ab + b² to find 11².
19. 19.If a + b = 11 and ab = 30, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 56 × 44.
21. 21.Use a² − b² = (a + b)(a − b) to find 57² − 16².
22. 22.Use (a + b)² = a² + 2ab + b² to find 55².
23. 23.Find the value of x² − y² when x = 4 and y = 3.
24. 24.Use (a + b)(a − b) = a² − b² to find 39 × 21.
25. 25.Use (a + b)(a − b) = a² − b² to find 63 × 57.
26. 26.Use (a + b)(a − b) = a² − b² to find 106 × 94.
27. 27.Use a² − b² = (a + b)(a − b) to find 73² − 2².
28. 28.Use a² − b² = (a + b)(a − b) to find 68² − 26².
29. 29.Use (a − b)² = a² − 2ab + b² to find 79².
30. 30.If a − b = 1 and ab = 6, what is a² + b²?
31. 31.If a + b = 10 and ab = 21, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 26 × 14.
33. 33.Use (a + b)² = a² + 2ab + b² to find 77².
34. 34.Use (a + b)² = a² + 2ab + b² to find 47².
35. 35.Use (a + b)² = a² + 2ab + b² to find 34².
36. 36.Use (a + b)(a − b) = a² − b² to find 76 × 64.
37. 37.Use a² − b² = (a + b)(a − b) to find 30² − 29².
38. 38.Find the value of x² + 2xy + y² when x = 3 and y = 2.
39. 39.Use (a − b)² = a² − 2ab + b² to find 47².
40. 40.Use (a + b)² = a² + 2ab + b² to find 88².

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