Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 741 · 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 83².
2. 2.If a + b = 9 and ab = 20, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 56².
4. 4.Use (a + b)(a − b) = a² − b² to find 32 × 28.
5. 5.Use (a − b)² = a² − 2ab + b² to find 28².
6. 6.Use a² − b² = (a + b)(a − b) to find 22² − 3².
7. 7.Use (a + b)(a − b) = a² − b² to find 21 × 19.
8. 8.Use (a − b)² = a² − 2ab + b² to find 71².
9. 9.If a + b = 13 and ab = 40, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 28².
11. 11.Find the value of x² − 2xy + y² when x = 13 and y = 7.
12. 12.Use (a + b)(a − b) = a² − b² to find 99 × 81.
13. 13.Find the value of x² − y² when x = 5 and y = 1.
14. 14.Use (a − b)² = a² − 2ab + b² to find 91².
15. 15.Use (a − b)² = a² − 2ab + b² to find 95².
16. 16.Use (a + b)(a − b) = a² − b² to find 22 × 18.
17. 17.Use (a − b)² = a² − 2ab + b² to find 47².
18. 18.Use (a − b)² = a² − 2ab + b² to find 69².
19. 19.Use a² − b² = (a + b)(a − b) to find 65² − 62².
20. 20.Use a² − b² = (a + b)(a − b) to find 40² − 14².
21. 21.If a + b = 5 and ab = 6, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 12 and y = 6.
23. 23.Use (a − b)² = a² − 2ab + b² to find 57².
24. 24.Use (a − b)² = a² − 2ab + b² to find 14².
25. 25.Find the value of x² + 2xy + y² when x = 12 and y = 3.
26. 26.Use a² − b² = (a + b)(a − b) to find 53² − 27².
27. 27.Use a² − b² = (a + b)(a − b) to find 97² − 77².
28. 28.Use (a + b)² = a² + 2ab + b² to find 103².
29. 29.Use (a − b)² = a² − 2ab + b² to find 29².
30. 30.Use (a − b)² = a² − 2ab + b² to find 34².
31. 31.If a − b = 1 and ab = 30, what is a² + b²?
32. 32.Find the value of x² − y² when x = 14 and y = 4.
33. 33.Use a² − b² = (a + b)(a − b) to find 86² − 24².
34. 34.Use (a + b)(a − b) = a² − b² to find 71 × 69.
35. 35.If a − b = 5 and ab = 24, what is a² + b²?
36. 36.If a − b = 3 and ab = 18, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 10 and y = 1.
38. 38.Use (a + b)(a − b) = a² − b² to find 68 × 52.
39. 39.If a + b = 10 and ab = 9, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 8 and y = 5.

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