Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 901 · 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 25².
2. 2.Use (a − b)² = a² − 2ab + b² to find 78².
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 46².
5. 5.Use (a − b)² = a² − 2ab + b² to find 25².
6. 6.Use (a + b)(a − b) = a² − b² to find 91 × 89.
7. 7.Use (a − b)² = a² − 2ab + b² to find 96².
8. 8.Use a² − b² = (a + b)(a − b) to find 80² − 23².
9. 9.Use (a − b)² = a² − 2ab + b² to find 81².
10. 10.Find the value of x² − 2xy + y² when x = 9 and y = 3.
11. 11.Use (a − b)² = a² − 2ab + b² to find 41².
12. 12.Find the value of x² − 2xy + y² when x = 9 and y = 7.
13. 13.Use (a + b)(a − b) = a² − b² to find 52 × 48.
14. 14.If a − b = 9 and ab = 10, what is a² + b²?
15. 15.Find the value of x² − y² when x = 13 and y = 3.
16. 16.Use (a − b)² = a² − 2ab + b² to find 21².
17. 17.Use (a + b)² = a² + 2ab + b² to find 89².
18. 18.If a + b = 15 and ab = 56, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 15 and y = 5.
20. 20.Use a² − b² = (a + b)(a − b) to find 50² − 21².
21. 21.If a + b = 13 and ab = 40, what is a² + b²?
22. 22.If a + b = 18 and ab = 77, what is a² + b²?
23. 23.If a − b = 1 and ab = 2, what is a² + b²?
24. 24.Find the value of x² − 2xy + y² when x = 7 and y = 4.
25. 25.Use a² − b² = (a + b)(a − b) to find 31² − 16².
26. 26.Use a² − b² = (a + b)(a − b) to find 74² − 25².
27. 27.Use a² − b² = (a + b)(a − b) to find 63² − 53².
28. 28.If a − b = 7 and ab = 8, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 31².
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 88² − 17².
32. 32.Find the value of x² + 2xy + y² when x = 15 and y = 2.
33. 33.If a − b = 3 and ab = 54, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 77² − 27².
35. 35.Find the value of x² − 2xy + y² when x = 9 and y = 5.
36. 36.Use a² − b² = (a + b)(a − b) to find 54² − 17².
37. 37.If a + b = 17 and ab = 72, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 77².
39. 39.If a + b = 12 and ab = 27, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 45 × 35.

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