Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 909 · 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 64².
2. 2.Use (a − b)² = a² − 2ab + b² to find 63².
3. 3.Use (a + b)² = a² + 2ab + b² to find 39².
4. 4.If a + b = 5 and ab = 6, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 24² − 20².
6. 6.If a − b = 8 and ab = 20, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 21².
8. 8.If a − b = 7 and ab = 44, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 50² − 13².
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 1.
11. 11.Find the value of x² + 2xy + y² when x = 11 and y = 8.
12. 12.Use (a − b)² = a² − 2ab + b² to find 32².
13. 13.Use a² − b² = (a + b)(a − b) to find 20² − 11².
14. 14.Use (a + b)(a − b) = a² − b² to find 47 × 33.
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Use a² − b² = (a + b)(a − b) to find 52² − 13².
17. 17.Use (a − b)² = a² − 2ab + b² to find 55².
18. 18.Use (a + b)² = a² + 2ab + b² to find 78².
19. 19.Use a² − b² = (a + b)(a − b) to find 63² − 18².
20. 20.Use (a − b)² = a² − 2ab + b² to find 39².
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 3.
22. 22.If a − b = 7 and ab = 8, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 85² − 13².
24. 24.Use (a + b)² = a² + 2ab + b² to find 32².
25. 25.Use (a − b)² = a² − 2ab + b² to find 51².
26. 26.Use (a + b)² = a² + 2ab + b² to find 55².
27. 27.If a + b = 12 and ab = 35, what is a² + b²?
28. 28.Find the value of x² − 2xy + y² when x = 4 and y = 2.
29. 29.Use a² − b² = (a + b)(a − b) to find 56² − 5².
30. 30.Find the value of x² − y² when x = 15 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 69².
32. 32.Use a² − b² = (a + b)(a − b) to find 40² − 27².
33. 33.Use (a − b)² = a² − 2ab + b² to find 99².
34. 34.Use (a + b)² = a² + 2ab + b² to find 52².
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 2.
36. 36.Use (a − b)² = a² − 2ab + b² to find 23².
37. 37.Use (a − b)² = a² − 2ab + b² to find 79².
38. 38.Use (a − b)² = a² − 2ab + b² to find 66².
39. 39.If a + b = 10 and ab = 21, what is a² + b²?
40. 40.Find the value of x² − y² when x = 12 and y = 9.

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