Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 176 · 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 a² − b² = (a + b)(a − b) to find 56² − 6².
2. 2.Use a² − b² = (a + b)(a − b) to find 47² − 5².
3. 3.If a − b = 10 and ab = 11, what is a² + b²?
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 96².
6. 6.Use (a + b)² = a² + 2ab + b² to find 79².
7. 7.Use (a + b)(a − b) = a² − b² to find 36 × 24.
8. 8.Use (a + b)(a − b) = a² − b² to find 81 × 79.
9. 9.Use a² − b² = (a + b)(a − b) to find 99² − 45².
10. 10.Find the value of x² − 2xy + y² when x = 11 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 46².
12. 12.Use (a − b)² = a² − 2ab + b² to find 37².
13. 13.Use (a − b)² = a² − 2ab + b² to find 26².
14. 14.Use (a − b)² = a² − 2ab + b² to find 77².
15. 15.If a + b = 14 and ab = 40, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 34 × 26.
17. 17.Use (a + b)² = a² + 2ab + b² to find 82².
18. 18.Use (a + b)(a − b) = a² − b² to find 67 × 53.
19. 19.Use (a + b)(a − b) = a² − b² to find 69 × 51.
20. 20.Use (a − b)² = a² − 2ab + b² to find 76².
21. 21.If a − b = 2 and ab = 8, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 61² − 1².
23. 23.Use (a − b)² = a² − 2ab + b² to find 78².
24. 24.Use (a + b)² = a² + 2ab + b² to find 23².
25. 25.Use (a − b)² = a² − 2ab + b² to find 75².
26. 26.Find the value of x² + 2xy + y² when x = 4 and y = 3.
27. 27.Use (a + b)² = a² + 2ab + b² to find 74².
28. 28.Use (a + b)² = a² + 2ab + b² to find 102².
29. 29.Use (a − b)² = a² − 2ab + b² to find 19².
30. 30.Use (a + b)(a − b) = a² − b² to find 49 × 31.
31. 31.Use a² − b² = (a + b)(a − b) to find 80² − 13².
32. 32.Use (a + b)² = a² + 2ab + b² to find 53².
33. 33.If a − b = 2 and ab = 3, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 35² − 9².
35. 35.Use a² − b² = (a + b)(a − b) to find 69² − 9².
36. 36.Use (a − b)² = a² − 2ab + b² to find 21².
37. 37.Use a² − b² = (a + b)(a − b) to find 51² − 22².
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 34².
40. 40.Use (a + b)(a − b) = a² − b² to find 35 × 25.

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