Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 313 · 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 59².
2. 2.If a + b = 6 and ab = 8, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 35² − 27².
4. 4.Use (a + b)(a − b) = a² − b² to find 102 × 98.
5. 5.Use (a + b)(a − b) = a² − b² to find 78 × 62.
6. 6.Use a² − b² = (a + b)(a − b) to find 50² − 32².
7. 7.Use (a + b)² = a² + 2ab + b² to find 78².
8. 8.Find the value of x² − y² when x = 5 and y = 4.
9. 9.If a + b = 5 and ab = 4, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 52².
11. 11.Use (a + b)(a − b) = a² − b² to find 103 × 97.
12. 12.Find the value of x² − 2xy + y² when x = 4 and y = 3.
13. 13.Use (a + b)(a − b) = a² − b² to find 62 × 58.
14. 14.Use (a − b)² = a² − 2ab + b² to find 31².
15. 15.If a − b = 5 and ab = 6, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 96².
17. 17.Find the value of x² + 2xy + y² when x = 4 and y = 3.
18. 18.Use (a − b)² = a² − 2ab + b² to find 86².
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 2.
20. 20.Find the value of x² − y² when x = 12 and y = 11.
21. 21.Use (a − b)² = a² − 2ab + b² to find 16².
22. 22.Use (a + b)² = a² + 2ab + b² to find 28².
23. 23.Use (a − b)² = a² − 2ab + b² to find 85².
24. 24.If a + b = 7 and ab = 6, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 22².
26. 26.Use (a + b)(a − b) = a² − b² to find 27 × 13.
27. 27.If a − b = 5 and ab = 24, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 33² − 8².
29. 29.Use (a − b)² = a² − 2ab + b² to find 92².
30. 30.Use a² − b² = (a + b)(a − b) to find 41² − 29².
31. 31.Use (a − b)² = a² − 2ab + b² to find 61².
32. 32.Use (a + b)² = a² + 2ab + b² to find 68².
33. 33.Find the value of x² − y² when x = 12 and y = 8.
34. 34.Use (a − b)² = a² − 2ab + b² to find 37².
35. 35.Use (a − b)² = a² − 2ab + b² to find 39².
36. 36.If a + b = 5 and ab = 6, what is a² + b²?
37. 37.If a − b = 2 and ab = 8, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 54².
39. 39.Use a² − b² = (a + b)(a − b) to find 78² − 35².
40. 40.Use (a + b)² = a² + 2ab + b² to find 67².

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