Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 950 · 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)(a − b) = a² − b² to find 48 × 32.
2. 2.Use (a + b)(a − b) = a² − b² to find 37 × 23.
3. 3.Use (a + b)² = a² + 2ab + b² to find 12².
4. 4.Use (a + b)(a − b) = a² − b² to find 28 × 12.
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 55².
7. 7.Find the value of x² + 2xy + y² when x = 9 and y = 1.
8. 8.Use (a + b)² = a² + 2ab + b² to find 19².
9. 9.Use (a + b)² = a² + 2ab + b² to find 97².
10. 10.Find the value of x² − 2xy + y² when x = 13 and y = 1.
11. 11.Use (a + b)² = a² + 2ab + b² to find 83².
12. 12.Use a² − b² = (a + b)(a − b) to find 84² − 45².
13. 13.Find the value of x² − y² when x = 8 and y = 4.
14. 14.Use (a + b)(a − b) = a² − b² to find 42 × 38.
15. 15.Use (a − b)² = a² − 2ab + b² to find 49².
16. 16.Use (a − b)² = a² − 2ab + b² to find 29².
17. 17.Use (a − b)² = a² − 2ab + b² to find 79².
18. 18.Use (a + b)² = a² + 2ab + b² to find 89².
19. 19.Use a² − b² = (a + b)(a − b) to find 34² − 16².
20. 20.If a − b = 2 and ab = 35, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 56² − 7².
22. 22.If a + b = 7 and ab = 12, what is a² + b²?
23. 23.If a + b = 3 and ab = 2, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 43².
25. 25.Use (a − b)² = a² − 2ab + b² to find 91².
26. 26.Use (a + b)(a − b) = a² − b² to find 53 × 47.
27. 27.If a − b = 8 and ab = 20, what is a² + b²?
28. 28.Find the value of x² − 2xy + y² when x = 4 and y = 3.
29. 29.Use a² − b² = (a + b)(a − b) to find 78² − 38².
30. 30.Use (a + b)(a − b) = a² − b² to find 82 × 78.
31. 31.If a − b = 1 and ab = 2, what is a² + b²?
32. 32.If a − b = 2 and ab = 8, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.Use a² − b² = (a + b)(a − b) to find 26² − 5².
35. 35.Use (a + b)(a − b) = a² − b² to find 64 × 56.
36. 36.Find the value of x² − 2xy + y² when x = 10 and y = 4.
37. 37.Find the value of x² − y² when x = 10 and y = 4.
38. 38.Use a² − b² = (a + b)(a − b) to find 32² − 22².
39. 39.Use (a + b)² = a² + 2ab + b² to find 53².
40. 40.If a − b = 6 and ab = 40, what is a² + b²?

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