Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 714 · 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.Use (a − b)² = a² − 2ab + b² to find 87².
2. 2.Use (a − b)² = a² − 2ab + b² to find 33².
3. 3.Use a² − b² = (a + b)(a − b) to find 24² − 23².
4. 4.If a − b = 8 and ab = 20, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 106 × 94.
6. 6.Use (a − b)² = a² − 2ab + b² to find 69².
7. 7.Use a² − b² = (a + b)(a − b) to find 97² − 96².
8. 8.Use (a + b)² = a² + 2ab + b² to find 54².
9. 9.Use (a − b)² = a² − 2ab + b² to find 11².
10. 10.Use a² − b² = (a + b)(a − b) to find 26² − 2².
11. 11.Find the value of x² + 2xy + y² when x = 5 and y = 4.
12. 12.Use (a − b)² = a² − 2ab + b² to find 42².
13. 13.Use a² − b² = (a + b)(a − b) to find 63² − 1².
14. 14.Find the value of x² − y² when x = 3 and y = 1.
15. 15.Find the value of x² − y² when x = 9 and y = 3.
16. 16.Use (a + b)(a − b) = a² − b² to find 65 × 55.
17. 17.Use (a + b)² = a² + 2ab + b² to find 73².
18. 18.If a − b = 5 and ab = 50, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 29².
20. 20.Use (a − b)² = a² − 2ab + b² to find 99².
21. 21.If a + b = 3 and ab = 2, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 82².
23. 23.Find the value of x² − 2xy + y² when x = 9 and y = 7.
24. 24.Use (a + b)² = a² + 2ab + b² to find 79².
25. 25.Use a² − b² = (a + b)(a − b) to find 85² − 65².
26. 26.Find the value of x² + 2xy + y² when x = 6 and y = 1.
27. 27.Use a² − b² = (a + b)(a − b) to find 59² − 11².
28. 28.Use a² − b² = (a + b)(a − b) to find 25² − 22².
29. 29.Use (a − b)² = a² − 2ab + b² to find 89².
30. 30.Use (a + b)(a − b) = a² − b² to find 85 × 75.
31. 31.Use (a − b)² = a² − 2ab + b² to find 44².
32. 32.Use (a + b)(a − b) = a² − b² to find 83 × 77.
33. 33.Use a² − b² = (a + b)(a − b) to find 64² − 11².
34. 34.Use a² − b² = (a + b)(a − b) to find 63² − 43².
35. 35.Use (a + b)² = a² + 2ab + b² to find 86².
36. 36.Use (a + b)² = a² + 2ab + b² to find 55².
37. 37.Use (a − b)² = a² − 2ab + b² to find 13².
38. 38.Find the value of x² − 2xy + y² when x = 7 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 61².
40. 40.Use (a + b)² = a² + 2ab + b² to find 66².

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