Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 95 · 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 60² − 11².
2. 2.Use (a + b)² = a² + 2ab + b² to find 73².
3. 3.Use (a + b)² = a² + 2ab + b² to find 76².
4. 4.Use (a + b)(a − b) = a² − b² to find 66 × 54.
5. 5.Use (a + b)² = a² + 2ab + b² to find 62².
6. 6.Use (a − b)² = a² − 2ab + b² to find 38².
7. 7.Use (a − b)² = a² − 2ab + b² to find 28².
8. 8.If a + b = 11 and ab = 24, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 43².
10. 10.Use (a + b)(a − b) = a² − b² to find 36 × 24.
11. 11.Use (a + b)(a − b) = a² − b² to find 89 × 71.
12. 12.Use (a − b)² = a² − 2ab + b² to find 44².
13. 13.If a + b = 14 and ab = 48, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 105 × 95.
15. 15.Use (a + b)(a − b) = a² − b² to find 22 × 18.
16. 16.Use (a + b)² = a² + 2ab + b² to find 105².
17. 17.Use (a − b)² = a² − 2ab + b² to find 88².
18. 18.If a + b = 10 and ab = 21, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 17².
20. 20.Find the value of x² − 2xy + y² when x = 6 and y = 1.
21. 21.Use (a + b)² = a² + 2ab + b² to find 106².
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 3.
23. 23.Use (a + b)(a − b) = a² − b² to find 52 × 48.
24. 24.If a + b = 5 and ab = 4, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 77².
26. 26.Use (a + b)(a − b) = a² − b² to find 44 × 36.
27. 27.Use (a − b)² = a² − 2ab + b² to find 48².
28. 28.If a − b = 2 and ab = 24, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 93² − 70².
30. 30.Use (a + b)² = a² + 2ab + b² to find 99².
31. 31.Use (a − b)² = a² − 2ab + b² to find 72².
32. 32.Use a² − b² = (a + b)(a − b) to find 58² − 12².
33. 33.Use (a + b)² = a² + 2ab + b² to find 12².
34. 34.Use (a + b)² = a² + 2ab + b² to find 36².
35. 35.Use (a + b)(a − b) = a² − b² to find 83 × 77.
36. 36.Find the value of x² − y² when x = 3 and y = 1.
37. 37.Find the value of x² − 2xy + y² when x = 11 and y = 1.
38. 38.Use a² − b² = (a + b)(a − b) to find 98² − 34².
39. 39.Use (a + b)(a − b) = a² − b² to find 64 × 56.
40. 40.Find the value of x² − y² when x = 14 and y = 6.

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