Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 413 · 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 a² − b² = (a + b)(a − b) to find 55² − 3².
2. 2.Find the value of x² − y² when x = 10 and y = 5.
3. 3.Use (a + b)² = a² + 2ab + b² to find 46².
4. 4.Use (a + b)(a − b) = a² − b² to find 41 × 39.
5. 5.Use (a + b)² = a² + 2ab + b² to find 81².
6. 6.Use (a + b)(a − b) = a² − b² to find 64 × 56.
7. 7.Find the value of x² − 2xy + y² when x = 13 and y = 10.
8. 8.Use a² − b² = (a + b)(a − b) to find 40² − 25².
9. 9.Use (a + b)(a − b) = a² − b² to find 107 × 93.
10. 10.Use (a + b)(a − b) = a² − b² to find 102 × 98.
11. 11.Use (a + b)² = a² + 2ab + b² to find 56².
12. 12.Use a² − b² = (a + b)(a − b) to find 98² − 94².
13. 13.Find the value of x² − 2xy + y² when x = 4 and y = 2.
14. 14.Find the value of x² + 2xy + y² when x = 8 and y = 7.
15. 15.Use (a + b)(a − b) = a² − b² to find 76 × 64.
16. 16.Use a² − b² = (a + b)(a − b) to find 59² − 31².
17. 17.If a + b = 18 and ab = 80, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 93 × 87.
19. 19.Use (a + b)² = a² + 2ab + b² to find 22².
20. 20.Find the value of x² − 2xy + y² when x = 15 and y = 5.
21. 21.Use (a + b)² = a² + 2ab + b² to find 91².
22. 22.Find the value of x² − 2xy + y² when x = 8 and y = 5.
23. 23.Use (a − b)² = a² − 2ab + b² to find 13².
24. 24.Use a² − b² = (a + b)(a − b) to find 42² − 10².
25. 25.If a + b = 4 and ab = 3, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 66 × 54.
27. 27.Use (a + b)(a − b) = a² − b² to find 81 × 79.
28. 28.Use (a − b)² = a² − 2ab + b² to find 56².
29. 29.Use (a − b)² = a² − 2ab + b² to find 31².
30. 30.Find the value of x² − y² when x = 7 and y = 3.
31. 31.If a + b = 10 and ab = 24, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 97².
33. 33.If a − b = 2 and ab = 8, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 60² − 5².
35. 35.Use (a − b)² = a² − 2ab + b² to find 99².
36. 36.Use (a + b)(a − b) = a² − b² to find 68 × 52.
37. 37.Find the value of x² − y² when x = 9 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 67² − 23².
39. 39.Use a² − b² = (a + b)(a − b) to find 89² − 29².
40. 40.Use (a − b)² = a² − 2ab + b² to find 71².

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