Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 854 · 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 13².
2. 2.Use (a + b)(a − b) = a² − b² to find 32 × 28.
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 35² − 31².
5. 5.If a + b = 5 and ab = 4, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 59² − 31².
7. 7.Use (a − b)² = a² − 2ab + b² to find 73².
8. 8.Use a² − b² = (a + b)(a − b) to find 75² − 6².
9. 9.Use (a + b)(a − b) = a² − b² to find 24 × 16.
10. 10.If a − b = 8 and ab = 20, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 48 × 32.
12. 12.If a − b = 2 and ab = 8, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 23².
14. 14.Use a² − b² = (a + b)(a − b) to find 55² − 7².
15. 15.If a + b = 13 and ab = 42, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 32².
17. 17.Use (a + b)² = a² + 2ab + b² to find 13².
18. 18.Use (a − b)² = a² − 2ab + b² to find 17².
19. 19.Find the value of x² − 2xy + y² when x = 13 and y = 5.
20. 20.Find the value of x² + 2xy + y² when x = 8 and y = 7.
21. 21.Use (a + b)² = a² + 2ab + b² to find 17².
22. 22.Use a² − b² = (a + b)(a − b) to find 81² − 52².
23. 23.Use a² − b² = (a + b)(a − b) to find 70² − 64².
24. 24.Use a² − b² = (a + b)(a − b) to find 99² − 64².
25. 25.Use (a + b)(a − b) = a² − b² to find 25 × 15.
26. 26.If a + b = 9 and ab = 8, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 65 × 55.
28. 28.Use (a + b)² = a² + 2ab + b² to find 83².
29. 29.Find the value of x² + 2xy + y² when x = 13 and y = 1.
30. 30.Use (a + b)² = a² + 2ab + b² to find 69².
31. 31.Use (a + b)(a − b) = a² − b² to find 92 × 88.
32. 32.Use a² − b² = (a + b)(a − b) to find 56² − 51².
33. 33.Use a² − b² = (a + b)(a − b) to find 87² − 60².
34. 34.Use (a − b)² = a² − 2ab + b² to find 99².
35. 35.Use (a + b)² = a² + 2ab + b² to find 96².
36. 36.Find the value of x² − 2xy + y² when x = 8 and y = 5.
37. 37.Use (a + b)(a − b) = a² − b² to find 61 × 59.
38. 38.Use (a + b)² = a² + 2ab + b² to find 74².
39. 39.If a + b = 9 and ab = 14, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 82² − 23².

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