Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 255 · 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 72².
2. 2.Use (a + b)² = a² + 2ab + b² to find 92².
3. 3.Find the value of x² + 2xy + y² when x = 12 and y = 8.
4. 4.If a − b = 1 and ab = 30, what is a² + b²?
5. 5.If a + b = 12 and ab = 11, what is a² + b²?
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 21².
8. 8.Use (a + b)(a − b) = a² − b² to find 82 × 78.
9. 9.Use (a + b)² = a² + 2ab + b² to find 81².
10. 10.Find the value of x² + 2xy + y² when x = 15 and y = 12.
11. 11.Use (a + b)² = a² + 2ab + b² to find 11².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 29².
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 92².
16. 16.Use a² − b² = (a + b)(a − b) to find 42² − 14².
17. 17.Use (a + b)² = a² + 2ab + b² to find 48².
18. 18.Find the value of x² − y² when x = 7 and y = 4.
19. 19.Use (a + b)² = a² + 2ab + b² to find 106².
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 3.
21. 21.Use (a − b)² = a² − 2ab + b² to find 73².
22. 22.Use (a + b)(a − b) = a² − b² to find 69 × 51.
23. 23.Use (a − b)² = a² − 2ab + b² to find 12².
24. 24.If a − b = 4 and ab = 32, what is a² + b²?
25. 25.If a − b = 1 and ab = 20, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 105 × 95.
27. 27.Use (a + b)² = a² + 2ab + b² to find 105².
28. 28.Use (a − b)² = a² − 2ab + b² to find 17².
29. 29.If a − b = 9 and ab = 10, what is a² + b²?
30. 30.If a − b = 5 and ab = 36, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 25².
32. 32.Use (a + b)(a − b) = a² − b² to find 91 × 89.
33. 33.If a − b = 3 and ab = 70, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 76² − 54².
35. 35.Use (a − b)² = a² − 2ab + b² to find 13².
36. 36.Use (a + b)(a − b) = a² − b² to find 44 × 36.
37. 37.Use (a + b)(a − b) = a² − b² to find 59 × 41.
38. 38.If a + b = 23 and ab = 132, what is a² + b²?
39. 39.Find the value of x² − y² when x = 14 and y = 12.
40. 40.Use a² − b² = (a + b)(a − b) to find 64² − 16².

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