Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 828 · 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 72² − 20².
2. 2.If a − b = 1 and ab = 20, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 98².
4. 4.Use (a + b)(a − b) = a² − b² to find 47 × 33.
5. 5.Use (a + b)² = a² + 2ab + b² to find 11².
6. 6.Find the value of x² − y² when x = 11 and y = 6.
7. 7.If a − b = 3 and ab = 10, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 16².
9. 9.Find the value of x² + 2xy + y² when x = 8 and y = 4.
10. 10.Use (a + b)² = a² + 2ab + b² to find 22².
11. 11.Use a² − b² = (a + b)(a − b) to find 84² − 62².
12. 12.Use (a + b)² = a² + 2ab + b² to find 17².
13. 13.Use (a + b)(a − b) = a² − b² to find 34 × 26.
14. 14.Use (a + b)(a − b) = a² − b² to find 91 × 89.
15. 15.If a + b = 21 and ab = 108, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 26².
17. 17.Find the value of x² − 2xy + y² when x = 7 and y = 4.
18. 18.Use (a − b)² = a² − 2ab + b² to find 35².
19. 19.Use (a + b)² = a² + 2ab + b² to find 28².
20. 20.Use (a − b)² = a² − 2ab + b² to find 39².
21. 21.Use (a + b)(a − b) = a² − b² to find 25 × 15.
22. 22.Use (a − b)² = a² − 2ab + b² to find 29².
23. 23.Use (a + b)² = a² + 2ab + b² to find 79².
24. 24.Use (a + b)² = a² + 2ab + b² to find 72².
25. 25.Find the value of x² + 2xy + y² when x = 9 and y = 6.
26. 26.Use (a + b)(a − b) = a² − b² to find 66 × 54.
27. 27.Use (a + b)² = a² + 2ab + b² to find 57².
28. 28.Use (a + b)(a − b) = a² − b² to find 31 × 29.
29. 29.Use (a + b)² = a² + 2ab + b² to find 32².
30. 30.Find the value of x² + 2xy + y² when x = 10 and y = 9.
31. 31.Use a² − b² = (a + b)(a − b) to find 62² − 55².
32. 32.Find the value of x² − 2xy + y² when x = 4 and y = 2.
33. 33.Use (a + b)(a − b) = a² − b² to find 51 × 49.
34. 34.Use (a − b)² = a² − 2ab + b² to find 62².
35. 35.Use (a + b)² = a² + 2ab + b² to find 38².
36. 36.Use a² − b² = (a + b)(a − b) to find 60² − 24².
37. 37.Find the value of x² + 2xy + y² when x = 12 and y = 10.
38. 38.Use (a + b)(a − b) = a² − b² to find 82 × 78.
39. 39.Use (a + b)(a − b) = a² − b² to find 21 × 19.
40. 40.Use (a + b)(a − b) = a² − b² to find 106 × 94.

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