Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 125 · 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 85².
2. 2.Find the value of x² − y² when x = 4 and y = 1.
3. 3.Use (a + b)(a − b) = a² − b² to find 51 × 49.
4. 4.Use (a − b)² = a² − 2ab + b² to find 83².
5. 5.Use a² − b² = (a + b)(a − b) to find 29² − 13².
6. 6.Use (a + b)(a − b) = a² − b² to find 69 × 51.
7. 7.Use (a + b)(a − b) = a² − b² to find 54 × 46.
8. 8.Use (a + b)(a − b) = a² − b² to find 105 × 95.
9. 9.Use (a − b)² = a² − 2ab + b² to find 61².
10. 10.Use a² − b² = (a + b)(a − b) to find 78² − 46².
11. 11.Use (a + b)(a − b) = a² − b² to find 56 × 44.
12. 12.Use (a + b)(a − b) = a² − b² to find 36 × 24.
13. 13.Use (a − b)² = a² − 2ab + b² to find 84².
14. 14.Use (a + b)² = a² + 2ab + b² to find 66².
15. 15.Find the value of x² − 2xy + y² when x = 6 and y = 1.
16. 16.Use (a + b)(a − b) = a² − b² to find 41 × 39.
17. 17.Find the value of x² + 2xy + y² when x = 14 and y = 11.
18. 18.Use (a − b)² = a² − 2ab + b² to find 22².
19. 19.If a − b = 1 and ab = 6, what is a² + b²?
20. 20.If a + b = 10 and ab = 16, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 43².
22. 22.Use (a + b)² = a² + 2ab + b² to find 56².
23. 23.Use (a − b)² = a² − 2ab + b² to find 15².
24. 24.Use a² − b² = (a + b)(a − b) to find 25² − 12².
25. 25.Use (a + b)(a − b) = a² − b² to find 106 × 94.
26. 26.Use a² − b² = (a + b)(a − b) to find 95² − 24².
27. 27.Use (a − b)² = a² − 2ab + b² to find 27².
28. 28.If a + b = 5 and ab = 4, what is a² + b²?
29. 29.Find the value of x² − y² when x = 15 and y = 7.
30. 30.If a − b = 2 and ab = 24, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 69².
32. 32.Find the value of x² + 2xy + y² when x = 8 and y = 1.
33. 33.Use (a + b)(a − b) = a² − b² to find 109 × 91.
34. 34.Use a² − b² = (a + b)(a − b) to find 34² − 2².
35. 35.If a − b = 3 and ab = 10, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 82 × 78.
37. 37.Use a² − b² = (a + b)(a − b) to find 94² − 54².
38. 38.Find the value of x² − y² when x = 5 and y = 2.
39. 39.Find the value of x² − 2xy + y² when x = 12 and y = 11.
40. 40.Use a² − b² = (a + b)(a − b) to find 76² − 4².

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