Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 353 · 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 31².
2. 2.Find the value of x² + 2xy + y² when x = 14 and y = 3.
3. 3.Use (a + b)(a − b) = a² − b² to find 81 × 79.
4. 4.Use (a + b)(a − b) = a² − b² to find 23 × 17.
5. 5.Find the value of x² − y² when x = 6 and y = 1.
6. 6.If a − b = 3 and ab = 18, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 27 × 13.
8. 8.Use a² − b² = (a + b)(a − b) to find 50² − 45².
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 91 × 89.
11. 11.Use (a + b)² = a² + 2ab + b² to find 87².
12. 12.Use (a − b)² = a² − 2ab + b² to find 15².
13. 13.If a + b = 9 and ab = 8, what is a² + b²?
14. 14.If a + b = 23 and ab = 132, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 108².
16. 16.Use (a + b)(a − b) = a² − b² to find 73 × 67.
17. 17.Use (a + b)² = a² + 2ab + b² to find 82².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 3.
19. 19.Find the value of x² + 2xy + y² when x = 6 and y = 5.
20. 20.Use (a + b)² = a² + 2ab + b² to find 29².
21. 21.Use (a − b)² = a² − 2ab + b² to find 28².
22. 22.If a − b = 1 and ab = 90, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 15 and y = 3.
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 13².
26. 26.Use (a − b)² = a² − 2ab + b² to find 49².
27. 27.Use (a − b)² = a² − 2ab + b² to find 51².
28. 28.Use (a + b)(a − b) = a² − b² to find 48 × 32.
29. 29.Find the value of x² − 2xy + y² when x = 11 and y = 5.
30. 30.Use a² − b² = (a + b)(a − b) to find 34² − 4².
31. 31.Use (a − b)² = a² − 2ab + b² to find 23².
32. 32.If a + b = 14 and ab = 24, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 39².
34. 34.Use a² − b² = (a + b)(a − b) to find 46² − 45².
35. 35.Use (a + b)(a − b) = a² − b² to find 78 × 62.
36. 36.Use (a + b)² = a² + 2ab + b² to find 77².
37. 37.If a + b = 7 and ab = 10, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 47².
39. 39.Use a² − b² = (a + b)(a − b) to find 20² − 8².
40. 40.Use (a + b)² = a² + 2ab + b² to find 53².

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