Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 526 · 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 64².
2. 2.Find the value of x² + 2xy + y² when x = 13 and y = 9.
3. 3.If a + b = 8 and ab = 15, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 101².
5. 5.If a + b = 22 and ab = 120, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 59 × 41.
7. 7.Use (a + b)(a − b) = a² − b² to find 53 × 47.
8. 8.Find the value of x² + 2xy + y² when x = 4 and y = 3.
9. 9.Find the value of x² + 2xy + y² when x = 5 and y = 1.
10. 10.Use (a + b)(a − b) = a² − b² to find 64 × 56.
11. 11.Use (a − b)² = a² − 2ab + b² to find 88².
12. 12.Use (a + b)(a − b) = a² − b² to find 29 × 11.
13. 13.If a + b = 5 and ab = 6, what is a² + b²?
14. 14.Find the value of x² − y² when x = 10 and y = 8.
15. 15.Use (a − b)² = a² − 2ab + b² to find 11².
16. 16.Use (a − b)² = a² − 2ab + b² to find 62².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 5.
18. 18.Use (a + b)² = a² + 2ab + b² to find 63².
19. 19.If a − b = 1 and ab = 2, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 6 and y = 4.
21. 21.Use (a − b)² = a² − 2ab + b² to find 82².
22. 22.Use (a + b)(a − b) = a² − b² to find 51 × 49.
23. 23.Find the value of x² − 2xy + y² when x = 12 and y = 10.
24. 24.Use (a + b)(a − b) = a² − b² to find 101 × 99.
25. 25.Use (a + b)² = a² + 2ab + b² to find 27².
26. 26.Use (a + b)(a − b) = a² − b² to find 105 × 95.
27. 27.Use (a + b)² = a² + 2ab + b² to find 36².
28. 28.If a + b = 7 and ab = 12, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 51².
30. 30.Use (a + b)(a − b) = a² − b² to find 41 × 39.
31. 31.Find the value of x² − 2xy + y² when x = 14 and y = 1.
32. 32.Use (a − b)² = a² − 2ab + b² to find 73².
33. 33.Use (a − b)² = a² − 2ab + b² to find 39².
34. 34.Use (a − b)² = a² − 2ab + b² to find 94².
35. 35.Find the value of x² + 2xy + y² when x = 3 and y = 1.
36. 36.Use (a − b)² = a² − 2ab + b² to find 13².
37. 37.Use a² − b² = (a + b)(a − b) to find 68² − 6².
38. 38.Find the value of x² + 2xy + y² when x = 5 and y = 2.
39. 39.Use (a − b)² = a² − 2ab + b² to find 53².
40. 40.Use (a + b)(a − b) = a² − b² to find 32 × 28.

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