Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 841 · 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 83².
2. 2.Use (a − b)² = a² − 2ab + b² to find 34².
3. 3.Use a² − b² = (a + b)(a − b) to find 23² − 22².
4. 4.Use (a + b)(a − b) = a² − b² to find 95 × 85.
5. 5.Use a² − b² = (a + b)(a − b) to find 48² − 27².
6. 6.Use (a + b)² = a² + 2ab + b² to find 108².
7. 7.Use (a − b)² = a² − 2ab + b² to find 13².
8. 8.Use a² − b² = (a + b)(a − b) to find 37² − 14².
9. 9.Find the value of x² − 2xy + y² when x = 5 and y = 2.
10. 10.Use (a + b)² = a² + 2ab + b² to find 32².
11. 11.Use (a + b)² = a² + 2ab + b² to find 38².
12. 12.Use a² − b² = (a + b)(a − b) to find 46² − 27².
13. 13.If a − b = 2 and ab = 63, what is a² + b²?
14. 14.If a − b = 3 and ab = 10, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 22².
16. 16.Use (a + b)(a − b) = a² − b² to find 27 × 13.
17. 17.Use (a + b)² = a² + 2ab + b² to find 39².
18. 18.Use a² − b² = (a + b)(a − b) to find 64² − 30².
19. 19.Use (a − b)² = a² − 2ab + b² to find 58².
20. 20.Use a² − b² = (a + b)(a − b) to find 59² − 5².
21. 21.Use a² − b² = (a + b)(a − b) to find 43² − 4².
22. 22.Use a² − b² = (a + b)(a − b) to find 70² − 11².
23. 23.Find the value of x² + 2xy + y² when x = 3 and y = 2.
24. 24.If a + b = 9 and ab = 8, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 55².
26. 26.If a + b = 5 and ab = 6, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 57² − 42².
28. 28.Use a² − b² = (a + b)(a − b) to find 25² − 11².
29. 29.Use a² − b² = (a + b)(a − b) to find 85² − 28².
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 6.
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 1.
32. 32.Find the value of x² − y² when x = 14 and y = 2.
33. 33.Find the value of x² − y² when x = 13 and y = 3.
34. 34.If a − b = 5 and ab = 24, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 26² − 12².
36. 36.Find the value of x² − y² when x = 7 and y = 5.
37. 37.Use (a − b)² = a² − 2ab + b² to find 37².
38. 38.If a − b = 1 and ab = 56, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 99 × 81.
40. 40.Use (a + b)² = a² + 2ab + b² to find 75².

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