Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 82 · 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 57².
2. 2.Use (a − b)² = a² − 2ab + b² to find 43².
3. 3.Use (a + b)(a − b) = a² − b² to find 92 × 88.
4. 4.Use (a + b)(a − b) = a² − b² to find 53 × 47.
5. 5.Use (a − b)² = a² − 2ab + b² to find 99².
6. 6.Use (a + b)² = a² + 2ab + b² to find 56².
7. 7.Use a² − b² = (a + b)(a − b) to find 37² − 31².
8. 8.Find the value of x² − 2xy + y² when x = 15 and y = 1.
9. 9.Use a² − b² = (a + b)(a − b) to find 84² − 72².
10. 10.Use a² − b² = (a + b)(a − b) to find 94² − 81².
11. 11.Use (a + b)² = a² + 2ab + b² to find 91².
12. 12.Use a² − b² = (a + b)(a − b) to find 81² − 69².
13. 13.Use (a − b)² = a² − 2ab + b² to find 33².
14. 14.Use a² − b² = (a + b)(a − b) to find 31² − 6².
15. 15.Use (a − b)² = a² − 2ab + b² to find 61².
16. 16.Find the value of x² − y² when x = 5 and y = 3.
17. 17.Use a² − b² = (a + b)(a − b) to find 56² − 44².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 13².
20. 20.Use (a + b)(a − b) = a² − b² to find 99 × 81.
21. 21.If a − b = 2 and ab = 63, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 24² − 3².
23. 23.Use (a − b)² = a² − 2ab + b² to find 89².
24. 24.If a − b = 4 and ab = 5, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 93 × 87.
26. 26.Find the value of x² + 2xy + y² when x = 11 and y = 6.
27. 27.Use (a − b)² = a² − 2ab + b² to find 79².
28. 28.Use (a + b)(a − b) = a² − b² to find 35 × 25.
29. 29.Find the value of x² − 2xy + y² when x = 12 and y = 1.
30. 30.Use a² − b² = (a + b)(a − b) to find 20² − 17².
31. 31.Find the value of x² + 2xy + y² when x = 10 and y = 2.
32. 32.Use (a + b)(a − b) = a² − b² to find 103 × 97.
33. 33.Use (a + b)² = a² + 2ab + b² to find 28².
34. 34.Use (a + b)² = a² + 2ab + b² to find 37².
35. 35.Use (a − b)² = a² − 2ab + b² to find 96².
36. 36.Use a² − b² = (a + b)(a − b) to find 29² − 2².
37. 37.Use (a − b)² = a² − 2ab + b² to find 45².
38. 38.Use (a + b)² = a² + 2ab + b² to find 95².
39. 39.Use a² − b² = (a + b)(a − b) to find 75² − 59².
40. 40.If a + b = 15 and ab = 56, what is a² + b²?

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