Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 727 · 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 29² − 4².
2. 2.Use (a + b)² = a² + 2ab + b² to find 38².
3. 3.Use (a − b)² = a² − 2ab + b² to find 15².
4. 4.Use (a − b)² = a² − 2ab + b² to find 84².
5. 5.Find the value of x² − y² when x = 5 and y = 1.
6. 6.If a − b = 4 and ab = 21, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 27² − 11².
8. 8.Find the value of x² − y² when x = 14 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 74 × 66.
10. 10.Use (a − b)² = a² − 2ab + b² to find 49².
11. 11.Use (a + b)(a − b) = a² − b² to find 35 × 25.
12. 12.Use (a − b)² = a² − 2ab + b² to find 77².
13. 13.Use (a − b)² = a² − 2ab + b² to find 32².
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.Find the value of x² + 2xy + y² when x = 11 and y = 9.
17. 17.Use (a − b)² = a² − 2ab + b² to find 85².
18. 18.If a − b = 2 and ab = 8, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 69².
20. 20.Find the value of x² − 2xy + y² when x = 7 and y = 6.
21. 21.If a − b = 5 and ab = 84, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 29².
23. 23.Use (a − b)² = a² − 2ab + b² to find 45².
24. 24.Use a² − b² = (a + b)(a − b) to find 58² − 2².
25. 25.If a − b = 2 and ab = 35, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 34².
27. 27.Use (a + b)² = a² + 2ab + b² to find 91².
28. 28.Use a² − b² = (a + b)(a − b) to find 22² − 6².
29. 29.Use (a − b)² = a² − 2ab + b² to find 93².
30. 30.Use (a − b)² = a² − 2ab + b² to find 86².
31. 31.If a − b = 2 and ab = 3, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 24².
33. 33.Find the value of x² − y² when x = 12 and y = 1.
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 6.
35. 35.Use a² − b² = (a + b)(a − b) to find 68² − 13².
36. 36.Use (a − b)² = a² − 2ab + b² to find 12².
37. 37.Use (a − b)² = a² − 2ab + b² to find 72².
38. 38.Use a² − b² = (a + b)(a − b) to find 24² − 10².
39. 39.Use a² − b² = (a + b)(a − b) to find 60² − 16².
40. 40.If a + b = 20 and ab = 96, what is a² + b²?

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