Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 609 · 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 = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 24² − 2².
3. 3.If a − b = 1 and ab = 90, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 29² − 13².
5. 5.Find the value of x² − y² when x = 9 and y = 1.
6. 6.Find the value of x² + 2xy + y² when x = 14 and y = 12.
7. 7.Find the value of x² + 2xy + y² when x = 8 and y = 5.
8. 8.Use (a + b)² = a² + 2ab + b² to find 85².
9. 9.Use a² − b² = (a + b)(a − b) to find 61² − 18².
10. 10.If a + b = 13 and ab = 40, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 97² − 75².
12. 12.Use a² − b² = (a + b)(a − b) to find 82² − 79².
13. 13.Use a² − b² = (a + b)(a − b) to find 23² − 10².
14. 14.Use (a + b)(a − b) = a² − b² to find 81 × 79.
15. 15.Find the value of x² − y² when x = 6 and y = 2.
16. 16.Use (a + b)(a − b) = a² − b² to find 106 × 94.
17. 17.Use (a + b)² = a² + 2ab + b² to find 34².
18. 18.Use (a − b)² = a² − 2ab + b² to find 27².
19. 19.Use (a + b)² = a² + 2ab + b² to find 35².
20. 20.Use (a + b)² = a² + 2ab + b² to find 42².
21. 21.Use a² − b² = (a + b)(a − b) to find 36² − 26².
22. 22.Use (a + b)(a − b) = a² − b² to find 31 × 29.
23. 23.Use (a + b)² = a² + 2ab + b² to find 18².
24. 24.Use a² − b² = (a + b)(a − b) to find 25² − 24².
25. 25.Use (a + b)(a − b) = a² − b² to find 23 × 17.
26. 26.Use (a + b)² = a² + 2ab + b² to find 27².
27. 27.Use (a − b)² = a² − 2ab + b² to find 73².
28. 28.Use (a − b)² = a² − 2ab + b² to find 82².
29. 29.Use (a + b)² = a² + 2ab + b² to find 12².
30. 30.Use (a − b)² = a² − 2ab + b² to find 99².
31. 31.Use (a + b)(a − b) = a² − b² to find 36 × 24.
32. 32.Use a² − b² = (a + b)(a − b) to find 67² − 25².
33. 33.Use (a + b)(a − b) = a² − b² to find 57 × 43.
34. 34.Use (a − b)² = a² − 2ab + b² to find 61².
35. 35.Find the value of x² − 2xy + y² when x = 10 and y = 4.
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 76².
38. 38.Use a² − b² = (a + b)(a − b) to find 25² − 22².
39. 39.Use (a + b)² = a² + 2ab + b² to find 14².
40. 40.Use (a + b)(a − b) = a² − b² to find 62 × 58.

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