Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 796 · 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 = 2 and ab = 15, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 68² − 14².
3. 3.Find the value of x² − 2xy + y² when x = 11 and y = 10.
4. 4.Find the value of x² + 2xy + y² when x = 14 and y = 3.
5. 5.Use (a − b)² = a² − 2ab + b² to find 12².
6. 6.Use (a + b)² = a² + 2ab + b² to find 44².
7. 7.Find the value of x² + 2xy + y² when x = 12 and y = 5.
8. 8.If a − b = 6 and ab = 40, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 88 × 72.
10. 10.Find the value of x² − y² when x = 3 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 16².
12. 12.If a + b = 6 and ab = 8, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 53².
14. 14.Use a² − b² = (a + b)(a − b) to find 30² − 20².
15. 15.Use (a + b)² = a² + 2ab + b² to find 93².
16. 16.Use (a + b)² = a² + 2ab + b² to find 75².
17. 17.Use (a + b)² = a² + 2ab + b² to find 107².
18. 18.Use (a − b)² = a² − 2ab + b² to find 21².
19. 19.Use (a − b)² = a² − 2ab + b² to find 36².
20. 20.Find the value of x² + 2xy + y² when x = 8 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 48².
22. 22.Use a² − b² = (a + b)(a − b) to find 23² − 11².
23. 23.Find the value of x² + 2xy + y² when x = 5 and y = 4.
24. 24.If a + b = 5 and ab = 6, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 82².
26. 26.Use (a + b)(a − b) = a² − b² to find 21 × 19.
27. 27.Use (a + b)(a − b) = a² − b² to find 61 × 59.
28. 28.Use (a − b)² = a² − 2ab + b² to find 37².
29. 29.Use (a − b)² = a² − 2ab + b² to find 43².
30. 30.Use a² − b² = (a + b)(a − b) to find 36² − 25².
31. 31.If a + b = 16 and ab = 60, what is a² + b²?
32. 32.Find the value of x² − 2xy + y² when x = 10 and y = 1.
33. 33.Use (a + b)(a − b) = a² − b² to find 36 × 24.
34. 34.Use (a − b)² = a² − 2ab + b² to find 22².
35. 35.Use (a − b)² = a² − 2ab + b² to find 82².
36. 36.Find the value of x² − 2xy + y² when x = 13 and y = 9.
37. 37.Use (a + b)² = a² + 2ab + b² to find 51².
38. 38.Use (a + b)² = a² + 2ab + b² to find 13².
39. 39.Use (a + b)² = a² + 2ab + b² to find 103².
40. 40.Use (a + b)² = a² + 2ab + b² to find 71².

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