Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 500 · 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 = 4 and ab = 12, what is a² + b²?
2. 2.If a + b = 13 and ab = 36, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 35².
4. 4.Use (a + b)(a − b) = a² − b² to find 103 × 97.
5. 5.Use a² − b² = (a + b)(a − b) to find 96² − 17².
6. 6.Use (a + b)(a − b) = a² − b² to find 36 × 24.
7. 7.Use (a + b)² = a² + 2ab + b² to find 21².
8. 8.Use (a − b)² = a² − 2ab + b² to find 45².
9. 9.Find the value of x² + 2xy + y² when x = 8 and y = 4.
10. 10.If a − b = 2 and ab = 8, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 23² − 6².
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 2.
13. 13.Find the value of x² − y² when x = 8 and y = 6.
14. 14.Use (a − b)² = a² − 2ab + b² to find 78².
15. 15.Use (a + b)² = a² + 2ab + b² to find 25².
16. 16.Use (a − b)² = a² − 2ab + b² to find 23².
17. 17.Use a² − b² = (a + b)(a − b) to find 41² − 24².
18. 18.Find the value of x² − y² when x = 8 and y = 1.
19. 19.Use (a + b)² = a² + 2ab + b² to find 36².
20. 20.Use a² − b² = (a + b)(a − b) to find 64² − 20².
21. 21.Find the value of x² − 2xy + y² when x = 10 and y = 6.
22. 22.Find the value of x² − y² when x = 12 and y = 3.
23. 23.Use a² − b² = (a + b)(a − b) to find 34² − 30².
24. 24.Use (a − b)² = a² − 2ab + b² to find 28².
25. 25.Use (a + b)(a − b) = a² − b² to find 34 × 26.
26. 26.Use (a − b)² = a² − 2ab + b² to find 39².
27. 27.Find the value of x² + 2xy + y² when x = 12 and y = 4.
28. 28.Find the value of x² + 2xy + y² when x = 15 and y = 11.
29. 29.Find the value of x² − 2xy + y² when x = 10 and y = 2.
30. 30.Use (a − b)² = a² − 2ab + b² to find 44².
31. 31.Find the value of x² − 2xy + y² when x = 8 and y = 2.
32. 32.Use (a + b)² = a² + 2ab + b² to find 108².
33. 33.Use (a − b)² = a² − 2ab + b² to find 21².
34. 34.Use a² − b² = (a + b)(a − b) to find 79² − 30².
35. 35.Use (a + b)² = a² + 2ab + b² to find 71².
36. 36.Use (a + b)² = a² + 2ab + b² to find 68².
37. 37.Find the value of x² − y² when x = 9 and y = 2.
38. 38.Use (a − b)² = a² − 2ab + b² to find 11².
39. 39.Use (a + b)² = a² + 2ab + b² to find 46².
40. 40.Use (a + b)² = a² + 2ab + b² to find 69².

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