Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 222 · 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 65² − 58².
2. 2.If a + b = 7 and ab = 6, what is a² + b²?
3. 3.Find the value of x² − 2xy + y² when x = 12 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 20² − 14².
5. 5.Use (a + b)(a − b) = a² − b² to find 45 × 35.
6. 6.Use (a − b)² = a² − 2ab + b² to find 33².
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 61².
9. 9.If a + b = 7 and ab = 12, what is a² + b²?
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 1.
11. 11.Use a² − b² = (a + b)(a − b) to find 85² − 9².
12. 12.Use (a − b)² = a² − 2ab + b² to find 86².
13. 13.Use (a − b)² = a² − 2ab + b² to find 63².
14. 14.Find the value of x² + 2xy + y² when x = 5 and y = 2.
15. 15.Use (a + b)² = a² + 2ab + b² to find 35².
16. 16.Use (a + b)(a − b) = a² − b² to find 101 × 99.
17. 17.Use a² − b² = (a + b)(a − b) to find 84² − 66².
18. 18.Find the value of x² + 2xy + y² when x = 15 and y = 6.
19. 19.Find the value of x² − y² when x = 6 and y = 4.
20. 20.Use a² − b² = (a + b)(a − b) to find 76² − 61².
21. 21.Use (a + b)(a − b) = a² − b² to find 83 × 77.
22. 22.Find the value of x² − y² when x = 8 and y = 4.
23. 23.Use a² − b² = (a + b)(a − b) to find 79² − 73².
24. 24.Use a² − b² = (a + b)(a − b) to find 57² − 9².
25. 25.Use (a + b)(a − b) = a² − b² to find 62 × 58.
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 25² − 19².
28. 28.Use (a + b)² = a² + 2ab + b² to find 19².
29. 29.Use a² − b² = (a + b)(a − b) to find 30² − 9².
30. 30.Use a² − b² = (a + b)(a − b) to find 48² − 27².
31. 31.Use (a − b)² = a² − 2ab + b² to find 51².
32. 32.Use (a + b)² = a² + 2ab + b² to find 21².
33. 33.Use (a + b)(a − b) = a² − b² to find 21 × 19.
34. 34.Find the value of x² − y² when x = 11 and y = 3.
35. 35.Use (a + b)² = a² + 2ab + b² to find 67².
36. 36.If a + b = 5 and ab = 4, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 49² − 34².
38. 38.Use a² − b² = (a + b)(a − b) to find 27² − 1².
39. 39.If a + b = 8 and ab = 7, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 81 × 79.

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