Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 649 · 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.If a − b = 9 and ab = 22, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 73².
3. 3.If a − b = 5 and ab = 50, what is a² + b²?
4. 4.Find the value of x² − y² when x = 8 and y = 1.
5. 5.Use (a + b)² = a² + 2ab + b² to find 81².
6. 6.If a − b = 2 and ab = 8, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 87².
8. 8.Use (a + b)(a − b) = a² − b² to find 37 × 23.
9. 9.Use (a + b)² = a² + 2ab + b² to find 69².
10. 10.Use (a + b)(a − b) = a² − b² to find 32 × 28.
11. 11.Use (a + b)² = a² + 2ab + b² to find 27².
12. 12.Find the value of x² + 2xy + y² when x = 10 and y = 3.
13. 13.Use (a − b)² = a² − 2ab + b² to find 19².
14. 14.Use (a + b)(a − b) = a² − b² to find 63 × 57.
15. 15.Use (a − b)² = a² − 2ab + b² to find 38².
16. 16.Use (a + b)² = a² + 2ab + b² to find 42².
17. 17.Use (a + b)² = a² + 2ab + b² to find 108².
18. 18.Use a² − b² = (a + b)(a − b) to find 75² − 4².
19. 19.Use (a − b)² = a² − 2ab + b² to find 36².
20. 20.Use a² − b² = (a + b)(a − b) to find 33² − 27².
21. 21.Use (a − b)² = a² − 2ab + b² to find 46².
22. 22.Use (a − b)² = a² − 2ab + b² to find 58².
23. 23.Use a² − b² = (a + b)(a − b) to find 92² − 3².
24. 24.Use (a + b)(a − b) = a² − b² to find 25 × 15.
25. 25.Use a² − b² = (a + b)(a − b) to find 22² − 2².
26. 26.Use (a − b)² = a² − 2ab + b² to find 45².
27. 27.Use (a − b)² = a² − 2ab + b² to find 57².
28. 28.Use (a + b)² = a² + 2ab + b² to find 72².
29. 29.Use a² − b² = (a + b)(a − b) to find 77² − 27².
30. 30.Find the value of x² − 2xy + y² when x = 9 and y = 3.
31. 31.Use (a + b)² = a² + 2ab + b² to find 84².
32. 32.Use (a − b)² = a² − 2ab + b² to find 84².
33. 33.If a − b = 1 and ab = 12, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 24 × 16.
35. 35.Use (a − b)² = a² − 2ab + b² to find 22².
36. 36.Find the value of x² + 2xy + y² when x = 14 and y = 6.
37. 37.Use a² − b² = (a + b)(a − b) to find 21² − 9².
38. 38.Find the value of x² − 2xy + y² when x = 3 and y = 1.
39. 39.Use a² − b² = (a + b)(a − b) to find 36² − 16².
40. 40.Use a² − b² = (a + b)(a − b) to find 51² − 25².

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