Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 510 · 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 46².
2. 2.Use (a + b)(a − b) = a² − b² to find 56 × 44.
3. 3.Use a² − b² = (a + b)(a − b) to find 21² − 8².
4. 4.If a − b = 7 and ab = 44, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 18².
6. 6.Use (a + b)² = a² + 2ab + b² to find 16².
7. 7.Use (a + b)² = a² + 2ab + b² to find 12².
8. 8.Use (a + b)(a − b) = a² − b² to find 69 × 51.
9. 9.Find the value of x² − 2xy + y² when x = 7 and y = 4.
10. 10.Find the value of x² + 2xy + y² when x = 4 and y = 3.
11. 11.Use (a − b)² = a² − 2ab + b² to find 96².
12. 12.Use (a − b)² = a² − 2ab + b² to find 12².
13. 13.If a − b = 4 and ab = 5, what is a² + b²?
14. 14.If a − b = 3 and ab = 10, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 45² − 20².
16. 16.Use (a + b)² = a² + 2ab + b² to find 81².
17. 17.Use a² − b² = (a + b)(a − b) to find 49² − 19².
18. 18.Use (a + b)(a − b) = a² − b² to find 23 × 17.
19. 19.Use a² − b² = (a + b)(a − b) to find 79² − 51².
20. 20.Use a² − b² = (a + b)(a − b) to find 68² − 42².
21. 21.Use a² − b² = (a + b)(a − b) to find 41² − 19².
22. 22.Use (a + b)² = a² + 2ab + b² to find 56².
23. 23.Use (a + b)(a − b) = a² − b² to find 78 × 62.
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 7².
25. 25.If a + b = 17 and ab = 60, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 86².
27. 27.Use a² − b² = (a + b)(a − b) to find 95² − 12².
28. 28.Use (a + b)(a − b) = a² − b² to find 52 × 48.
29. 29.Use a² − b² = (a + b)(a − b) to find 48² − 45².
30. 30.Use (a − b)² = a² − 2ab + b² to find 87².
31. 31.Use (a − b)² = a² − 2ab + b² to find 33².
32. 32.Find the value of x² + 2xy + y² when x = 14 and y = 3.
33. 33.If a − b = 1 and ab = 12, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 21².
35. 35.If a − b = 1 and ab = 2, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 97² − 96².
37. 37.Find the value of x² − 2xy + y² when x = 9 and y = 4.
38. 38.Use a² − b² = (a + b)(a − b) to find 81² − 64².
39. 39.Use a² − b² = (a + b)(a − b) to find 73² − 1².
40. 40.Use (a + b)² = a² + 2ab + b² to find 64².

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