Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 256 · 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 35².
2. 2.Use a² − b² = (a + b)(a − b) to find 38² − 9².
3. 3.Use (a − b)² = a² − 2ab + b² to find 96².
4. 4.Use a² − b² = (a + b)(a − b) to find 48² − 26².
5. 5.Use (a − b)² = a² − 2ab + b² to find 28².
6. 6.Find the value of x² − 2xy + y² when x = 7 and y = 2.
7. 7.Use (a − b)² = a² − 2ab + b² to find 29².
8. 8.Use (a + b)² = a² + 2ab + b² to find 34².
9. 9.Use (a − b)² = a² − 2ab + b² to find 53².
10. 10.Find the value of x² − y² when x = 5 and y = 1.
11. 11.Find the value of x² − y² when x = 3 and y = 2.
12. 12.Find the value of x² − y² when x = 4 and y = 1.
13. 13.Use (a + b)(a − b) = a² − b² to find 48 × 32.
14. 14.Use (a + b)(a − b) = a² − b² to find 31 × 29.
15. 15.Use a² − b² = (a + b)(a − b) to find 32² − 11².
16. 16.If a − b = 7 and ab = 8, what is a² + b²?
17. 17.Find the value of x² − y² when x = 5 and y = 3.
18. 18.Find the value of x² − 2xy + y² when x = 11 and y = 10.
19. 19.Use (a + b)² = a² + 2ab + b² to find 32².
20. 20.If a − b = 10 and ab = 24, what is a² + b²?
21. 21.If a − b = 3 and ab = 28, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 25².
23. 23.Use a² − b² = (a + b)(a − b) to find 97² − 17².
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 11².
25. 25.Find the value of x² − y² when x = 14 and y = 4.
26. 26.Find the value of x² − 2xy + y² when x = 14 and y = 10.
27. 27.Use (a − b)² = a² − 2ab + b² to find 31².
28. 28.Use (a + b)(a − b) = a² − b² to find 51 × 49.
29. 29.If a + b = 16 and ab = 55, what is a² + b²?
30. 30.Find the value of x² + 2xy + y² when x = 6 and y = 1.
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 4.
32. 32.Use (a + b)² = a² + 2ab + b² to find 28².
33. 33.Use (a − b)² = a² − 2ab + b² to find 36².
34. 34.Find the value of x² − y² when x = 8 and y = 1.
35. 35.Use (a − b)² = a² − 2ab + b² to find 44².
36. 36.If a + b = 5 and ab = 6, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 6.
38. 38.Use (a − b)² = a² − 2ab + b² to find 27².
39. 39.Use (a + b)(a − b) = a² − b² to find 104 × 96.
40. 40.Use (a + b)² = a² + 2ab + b² to find 62².

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