Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 748 · 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 53².
2. 2.Use a² − b² = (a + b)(a − b) to find 39² − 28².
3. 3.Use (a + b)² = a² + 2ab + b² to find 52².
4. 4.Find the value of x² − 2xy + y² when x = 11 and y = 9.
5. 5.Use (a + b)(a − b) = a² − b² to find 105 × 95.
6. 6.Use (a + b)² = a² + 2ab + b² to find 42².
7. 7.Use (a + b)(a − b) = a² − b² to find 55 × 45.
8. 8.Use (a + b)(a − b) = a² − b² to find 28 × 12.
9. 9.Use (a + b)² = a² + 2ab + b² to find 107².
10. 10.Find the value of x² + 2xy + y² when x = 8 and y = 2.
11. 11.Use (a + b)(a − b) = a² − b² to find 24 × 16.
12. 12.Use (a + b)² = a² + 2ab + b² to find 13².
13. 13.If a − b = 7 and ab = 30, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 52².
15. 15.Use a² − b² = (a + b)(a − b) to find 81² − 31².
16. 16.Find the value of x² + 2xy + y² when x = 15 and y = 12.
17. 17.Use a² − b² = (a + b)(a − b) to find 81² − 46².
18. 18.Use (a − b)² = a² − 2ab + b² to find 34².
19. 19.If a + b = 4 and ab = 3, what is a² + b²?
20. 20.If a + b = 12 and ab = 11, what is a² + b²?
21. 21.Find the value of x² − 2xy + y² when x = 13 and y = 8.
22. 22.Use (a − b)² = a² − 2ab + b² to find 56².
23. 23.Use (a + b)(a − b) = a² − b² to find 71 × 69.
24. 24.If a + b = 20 and ab = 99, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 31 × 29.
26. 26.Find the value of x² − y² when x = 13 and y = 8.
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 7.
28. 28.Use (a + b)² = a² + 2ab + b² to find 75².
29. 29.Use (a − b)² = a² − 2ab + b² to find 76².
30. 30.Use (a − b)² = a² − 2ab + b² to find 68².
31. 31.Use a² − b² = (a + b)(a − b) to find 50² − 26².
32. 32.Use (a + b)² = a² + 2ab + b² to find 78².
33. 33.Use (a + b)(a − b) = a² − b² to find 22 × 18.
34. 34.If a + b = 6 and ab = 8, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 20² − 19².
36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 2.
37. 37.Use a² − b² = (a + b)(a − b) to find 91² − 87².
38. 38.Use (a + b)² = a² + 2ab + b² to find 73².
39. 39.Use (a + b)(a − b) = a² − b² to find 61 × 59.
40. 40.Find the value of x² − y² when x = 12 and y = 10.

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