Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 323 · 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 = 12 and ab = 32, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 5 and y = 1.
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 67².
5. 5.Use (a − b)² = a² − 2ab + b² to find 19².
6. 6.If a + b = 8 and ab = 7, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 106².
8. 8.Use (a − b)² = a² − 2ab + b² to find 59².
9. 9.Use (a + b)(a − b) = a² − b² to find 72 × 68.
10. 10.Use (a + b)(a − b) = a² − b² to find 83 × 77.
11. 11.Use (a + b)² = a² + 2ab + b² to find 71².
12. 12.Use (a − b)² = a² − 2ab + b² to find 94².
13. 13.Use (a − b)² = a² − 2ab + b² to find 46².
14. 14.Use a² − b² = (a + b)(a − b) to find 28² − 24².
15. 15.Use (a + b)² = a² + 2ab + b² to find 88².
16. 16.Use (a + b)² = a² + 2ab + b² to find 92².
17. 17.Find the value of x² − y² when x = 10 and y = 1.
18. 18.Use (a − b)² = a² − 2ab + b² to find 53².
19. 19.Use (a − b)² = a² − 2ab + b² to find 49².
20. 20.Use a² − b² = (a + b)(a − b) to find 82² − 20².
21. 21.Find the value of x² + 2xy + y² when x = 15 and y = 2.
22. 22.Use (a + b)(a − b) = a² − b² to find 28 × 12.
23. 23.Use a² − b² = (a + b)(a − b) to find 66² − 56².
24. 24.Find the value of x² − 2xy + y² when x = 8 and y = 1.
25. 25.Use (a + b)² = a² + 2ab + b² to find 36².
26. 26.Use (a − b)² = a² − 2ab + b² to find 15².
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 1.
28. 28.Find the value of x² − y² when x = 5 and y = 3.
29. 29.Use (a + b)² = a² + 2ab + b² to find 107².
30. 30.If a − b = 4 and ab = 5, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 13².
32. 32.Use (a − b)² = a² − 2ab + b² to find 32².
33. 33.Use (a + b)(a − b) = a² − b² to find 79 × 61.
34. 34.Use (a − b)² = a² − 2ab + b² to find 83².
35. 35.Find the value of x² − y² when x = 8 and y = 2.
36. 36.Use (a + b)² = a² + 2ab + b² to find 39².
37. 37.Use (a − b)² = a² − 2ab + b² to find 39².
38. 38.Use (a + b)(a − b) = a² − b² to find 62 × 58.
39. 39.Use (a − b)² = a² − 2ab + b² to find 55².
40. 40.Use (a − b)² = a² − 2ab + b² to find 63².

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