Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 410 · 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)² = a² + 2ab + b² to find 66².
2. 2.Use (a + b)(a − b) = a² − b² to find 27 × 13.
3. 3.Use (a + b)² = a² + 2ab + b² to find 64².
4. 4.Use (a − b)² = a² − 2ab + b² to find 67².
5. 5.Use (a + b)² = a² + 2ab + b² to find 11².
6. 6.If a + b = 10 and ab = 9, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 73².
8. 8.Use (a + b)(a − b) = a² − b² to find 72 × 68.
9. 9.Use a² − b² = (a + b)(a − b) to find 87² − 54².
10. 10.Use (a − b)² = a² − 2ab + b² to find 83².
11. 11.Use a² − b² = (a + b)(a − b) to find 64² − 63².
12. 12.Use (a − b)² = a² − 2ab + b² to find 37².
13. 13.Use (a + b)² = a² + 2ab + b² to find 89².
14. 14.Use (a − b)² = a² − 2ab + b² to find 38².
15. 15.If a + b = 11 and ab = 30, what is a² + b²?
16. 16.If a + b = 15 and ab = 54, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 97².
18. 18.If a + b = 11 and ab = 10, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 98².
20. 20.Use a² − b² = (a + b)(a − b) to find 38² − 9².
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 39².
22. 22.Find the value of x² + 2xy + y² when x = 12 and y = 9.
23. 23.Use (a − b)² = a² − 2ab + b² to find 34².
24. 24.Use (a + b)(a − b) = a² − b² to find 48 × 32.
25. 25.Use (a − b)² = a² − 2ab + b² to find 57².
26. 26.Find the value of x² − 2xy + y² when x = 12 and y = 10.
27. 27.Use (a + b)² = a² + 2ab + b² to find 32².
28. 28.Use (a + b)² = a² + 2ab + b² to find 26².
29. 29.Use (a + b)² = a² + 2ab + b² to find 24².
30. 30.Use (a − b)² = a² − 2ab + b² to find 17².
31. 31.Use a² − b² = (a + b)(a − b) to find 39² − 6².
32. 32.Use a² − b² = (a + b)(a − b) to find 75² − 74².
33. 33.Use (a + b)² = a² + 2ab + b² to find 74².
34. 34.Use (a + b)(a − b) = a² − b² to find 58 × 42.
35. 35.Use (a − b)² = a² − 2ab + b² to find 55².
36. 36.Find the value of x² − 2xy + y² when x = 15 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 80² − 1².
38. 38.Use (a + b)² = a² + 2ab + b² to find 49².
39. 39.Use (a + b)(a − b) = a² − b² to find 105 × 95.
40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 1.

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