Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 288 · 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)(a − b) = a² − b² to find 91 × 89.
2. 2.Use (a − b)² = a² − 2ab + b² to find 53².
3. 3.Use (a + b)(a − b) = a² − b² to find 105 × 95.
4. 4.If a + b = 14 and ab = 33, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
6. 6.Use (a + b)(a − b) = a² − b² to find 69 × 51.
7. 7.Use (a − b)² = a² − 2ab + b² to find 71².
8. 8.Use (a + b)(a − b) = a² − b² to find 34 × 26.
9. 9.Use (a + b)(a − b) = a² − b² to find 61 × 59.
10. 10.If a − b = 1 and ab = 2, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 63² − 25².
12. 12.Use a² − b² = (a + b)(a − b) to find 33² − 10².
13. 13.Find the value of x² − y² when x = 15 and y = 8.
14. 14.Use (a + b)² = a² + 2ab + b² to find 22².
15. 15.If a + b = 6 and ab = 5, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 97² − 80².
17. 17.Use (a + b)² = a² + 2ab + b² to find 105².
18. 18.Find the value of x² − 2xy + y² when x = 3 and y = 1.
19. 19.Use (a − b)² = a² − 2ab + b² to find 35².
20. 20.If a − b = 4 and ab = 5, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 29 × 11.
22. 22.Find the value of x² − y² when x = 14 and y = 12.
23. 23.Use a² − b² = (a + b)(a − b) to find 85² − 38².
24. 24.If a + b = 13 and ab = 40, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 95 × 85.
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 52².
28. 28.Use (a − b)² = a² − 2ab + b² to find 67².
29. 29.Use a² − b² = (a + b)(a − b) to find 39² − 14².
30. 30.Use (a + b)² = a² + 2ab + b² to find 69².
31. 31.Use (a + b)(a − b) = a² − b² to find 43 × 37.
32. 32.Find the value of x² + 2xy + y² when x = 4 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 32².
34. 34.Use (a − b)² = a² − 2ab + b² to find 51².
35. 35.Use (a + b)² = a² + 2ab + b² to find 63².
36. 36.Use a² − b² = (a + b)(a − b) to find 83² − 47².
37. 37.Use (a − b)² = a² − 2ab + b² to find 15².
38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 10.
39. 39.Use (a + b)(a − b) = a² − b² to find 82 × 78.
40. 40.Use (a + b)(a − b) = a² − b² to find 94 × 86.

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