Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 861 · 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 = 11 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 49² − 8².
3. 3.If a − b = 2 and ab = 15, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 81² − 5².
5. 5.Use (a + b)² = a² + 2ab + b² to find 102².
6. 6.Use (a + b)(a − b) = a² − b² to find 82 × 78.
7. 7.Use (a + b)(a − b) = a² − b² to find 98 × 82.
8. 8.Use (a + b)(a − b) = a² − b² to find 25 × 15.
9. 9.Use (a − b)² = a² − 2ab + b² to find 13².
10. 10.Use a² − b² = (a + b)(a − b) to find 44² − 18².
11. 11.Find the value of x² − 2xy + y² when x = 7 and y = 6.
12. 12.Use (a + b)² = a² + 2ab + b² to find 57².
13. 13.Use (a − b)² = a² − 2ab + b² to find 56².
14. 14.Use a² − b² = (a + b)(a − b) to find 31² − 7².
15. 15.Use a² − b² = (a + b)(a − b) to find 34² − 20².
16. 16.Find the value of x² + 2xy + y² when x = 9 and y = 4.
17. 17.Use a² − b² = (a + b)(a − b) to find 29² − 8².
18. 18.Use (a + b)(a − b) = a² − b² to find 59 × 41.
19. 19.Use (a + b)² = a² + 2ab + b² to find 32².
20. 20.Find the value of x² − y² when x = 3 and y = 1.
21. 21.If a − b = 9 and ab = 10, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 27² − 1².
23. 23.Use (a + b)(a − b) = a² − b² to find 97 × 83.
24. 24.If a − b = 1 and ab = 12, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 16².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 8 and y = 1.
28. 28.If a − b = 6 and ab = 7, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 66² − 47².
30. 30.Use (a − b)² = a² − 2ab + b² to find 34².
31. 31.Use (a − b)² = a² − 2ab + b² to find 39².
32. 32.Use (a + b)² = a² + 2ab + b² to find 24².
33. 33.Use (a + b)² = a² + 2ab + b² to find 77².
34. 34.Use (a + b)(a − b) = a² − b² to find 61 × 59.
35. 35.Use (a − b)² = a² − 2ab + b² to find 96².
36. 36.Use (a + b)(a − b) = a² − b² to find 99 × 81.
37. 37.If a + b = 19 and ab = 88, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 97² − 7².
39. 39.Use (a + b)² = a² + 2ab + b² to find 54².
40. 40.Use (a − b)² = a² − 2ab + b² to find 97².

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