Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 576 · 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 a² − b² = (a + b)(a − b) to find 53² − 49².
2. 2.Use a² − b² = (a + b)(a − b) to find 98² − 26².
3. 3.Use a² − b² = (a + b)(a − b) to find 55² − 5².
4. 4.Use (a − b)² = a² − 2ab + b² to find 79².
5. 5.Use (a + b)² = a² + 2ab + b² to find 15².
6. 6.Find the value of x² − y² when x = 15 and y = 1.
7. 7.Use a² − b² = (a + b)(a − b) to find 72² − 27².
8. 8.Find the value of x² + 2xy + y² when x = 11 and y = 6.
9. 9.Find the value of x² − y² when x = 3 and y = 1.
10. 10.Find the value of x² + 2xy + y² when x = 10 and y = 4.
11. 11.Find the value of x² − y² when x = 11 and y = 6.
12. 12.Use (a + b)(a − b) = a² − b² to find 109 × 91.
13. 13.Use a² − b² = (a + b)(a − b) to find 36² − 3².
14. 14.Use a² − b² = (a + b)(a − b) to find 22² − 18².
15. 15.Use (a + b)² = a² + 2ab + b² to find 85².
16. 16.Use (a − b)² = a² − 2ab + b² to find 36².
17. 17.Find the value of x² − 2xy + y² when x = 13 and y = 5.
18. 18.Find the value of x² − 2xy + y² when x = 3 and y = 2.
19. 19.If a + b = 8 and ab = 7, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 19².
21. 21.If a − b = 4 and ab = 21, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 17².
23. 23.Use a² − b² = (a + b)(a − b) to find 30² − 24².
24. 24.Use (a + b)² = a² + 2ab + b² to find 53².
25. 25.Use a² − b² = (a + b)(a − b) to find 62² − 2².
26. 26.If a + b = 12 and ab = 27, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 31².
28. 28.Use a² − b² = (a + b)(a − b) to find 54² − 37².
29. 29.Use (a − b)² = a² − 2ab + b² to find 23².
30. 30.Use (a + b)² = a² + 2ab + b² to find 39².
31. 31.Use (a + b)(a − b) = a² − b² to find 72 × 68.
32. 32.Use a² − b² = (a + b)(a − b) to find 53² − 33².
33. 33.Use (a + b)(a − b) = a² − b² to find 102 × 98.
34. 34.Use (a − b)² = a² − 2ab + b² to find 22².
35. 35.Use (a + b)(a − b) = a² − b² to find 32 × 28.
36. 36.If a + b = 4 and ab = 3, what is a² + b²?
37. 37.Find the value of x² − 2xy + y² when x = 13 and y = 11.
38. 38.Use (a + b)(a − b) = a² − b² to find 54 × 46.
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 7.
40. 40.Use (a + b)² = a² + 2ab + b² to find 52².

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