Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 249 · 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 64².
2. 2.Use (a − b)² = a² − 2ab + b² to find 17².
3. 3.Use (a + b)(a − b) = a² − b² to find 45 × 35.
4. 4.Use (a + b)² = a² + 2ab + b² to find 12².
5. 5.Use (a − b)² = a² − 2ab + b² to find 34².
6. 6.Use (a − b)² = a² − 2ab + b² to find 73².
7. 7.Use a² − b² = (a + b)(a − b) to find 24² − 3².
8. 8.If a − b = 4 and ab = 77, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 102 × 98.
10. 10.If a + b = 16 and ab = 55, what is a² + b²?
11. 11.If a + b = 4 and ab = 3, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 20² − 2².
13. 13.Use (a + b)² = a² + 2ab + b² to find 88².
14. 14.Find the value of x² − 2xy + y² when x = 10 and y = 6.
15. 15.Use (a + b)(a − b) = a² − b² to find 83 × 77.
16. 16.Find the value of x² − y² when x = 15 and y = 12.
17. 17.Use a² − b² = (a + b)(a − b) to find 21² − 12².
18. 18.Use a² − b² = (a + b)(a − b) to find 59² − 25².
19. 19.Use (a − b)² = a² − 2ab + b² to find 94².
20. 20.Find the value of x² − y² when x = 5 and y = 1.
21. 21.Use a² − b² = (a + b)(a − b) to find 99² − 91².
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 8.
23. 23.If a − b = 2 and ab = 48, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 38 × 22.
25. 25.Use (a + b)² = a² + 2ab + b² to find 39².
26. 26.Use a² − b² = (a + b)(a − b) to find 75² − 37².
27. 27.Use (a − b)² = a² − 2ab + b² to find 22².
28. 28.Use (a + b)² = a² + 2ab + b² to find 72².
29. 29.If a + b = 13 and ab = 30, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 94² − 71².
31. 31.Use (a − b)² = a² − 2ab + b² to find 33².
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.If a − b = 2 and ab = 99, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 77².
35. 35.Use a² − b² = (a + b)(a − b) to find 46² − 20².
36. 36.Use (a − b)² = a² − 2ab + b² to find 45².
37. 37.Use (a − b)² = a² − 2ab + b² to find 86².
38. 38.Find the value of x² − 2xy + y² when x = 8 and y = 2.
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 15 and y = 13.

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