Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 59 · 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 a² − b² = (a + b)(a − b) to find 87² − 39².
2. 2.Find the value of x² − 2xy + y² when x = 15 and y = 3.
3. 3.Use (a + b)² = a² + 2ab + b² to find 47².
4. 4.Use (a − b)² = a² − 2ab + b² to find 78².
5. 5.Use (a − b)² = a² − 2ab + b² to find 39².
6. 6.Use (a − b)² = a² − 2ab + b² to find 53².
7. 7.Find the value of x² + 2xy + y² when x = 7 and y = 6.
8. 8.Use (a − b)² = a² − 2ab + b² to find 29².
9. 9.Use (a − b)² = a² − 2ab + b² to find 52².
10. 10.Use (a + b)(a − b) = a² − b² to find 81 × 79.
11. 11.Find the value of x² − y² when x = 15 and y = 10.
12. 12.Use (a + b)(a − b) = a² − b² to find 67 × 53.
13. 13.If a + b = 5 and ab = 4, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 33².
15. 15.Use a² − b² = (a + b)(a − b) to find 50² − 26².
16. 16.If a − b = 5 and ab = 84, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 42² − 28².
18. 18.Use a² − b² = (a + b)(a − b) to find 32² − 23².
19. 19.If a − b = 6 and ab = 16, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 32 × 28.
21. 21.Use (a − b)² = a² − 2ab + b² to find 84².
22. 22.Find the value of x² − y² when x = 14 and y = 10.
23. 23.Use (a + b)(a − b) = a² − b² to find 104 × 96.
24. 24.Use a² − b² = (a + b)(a − b) to find 62² − 19².
25. 25.If a + b = 10 and ab = 16, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 22².
27. 27.If a + b = 19 and ab = 84, what is a² + b²?
28. 28.If a − b = 1 and ab = 12, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 64².
30. 30.Use (a + b)² = a² + 2ab + b² to find 63².
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 1.
32. 32.Find the value of x² − 2xy + y² when x = 15 and y = 4.
33. 33.Use (a − b)² = a² − 2ab + b² to find 36².
34. 34.Use (a − b)² = a² − 2ab + b² to find 79².
35. 35.If a − b = 9 and ab = 22, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 71².
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 33².
39. 39.Find the value of x² − y² when x = 4 and y = 1.
40. 40.Use a² − b² = (a + b)(a − b) to find 27² − 5².

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