Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 84 · 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 38².
2. 2.Use (a + b)² = a² + 2ab + b² to find 109².
3. 3.Use a² − b² = (a + b)(a − b) to find 80² − 39².
4. 4.Use (a − b)² = a² − 2ab + b² to find 61².
5. 5.Use a² − b² = (a + b)(a − b) to find 97² − 96².
6. 6.Use a² − b² = (a + b)(a − b) to find 89² − 8².
7. 7.Use (a − b)² = a² − 2ab + b² to find 87².
8. 8.Find the value of x² − y² when x = 3 and y = 2.
9. 9.Find the value of x² + 2xy + y² when x = 15 and y = 2.
10. 10.Use (a − b)² = a² − 2ab + b² to find 38².
11. 11.Use (a + b)(a − b) = a² − b² to find 28 × 12.
12. 12.Find the value of x² + 2xy + y² when x = 5 and y = 3.
13. 13.Use a² − b² = (a + b)(a − b) to find 70² − 54².
14. 14.Find the value of x² + 2xy + y² when x = 7 and y = 2.
15. 15.If a − b = 8 and ab = 9, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 88².
17. 17.Use (a + b)(a − b) = a² − b² to find 79 × 61.
18. 18.Use a² − b² = (a + b)(a − b) to find 77² − 23².
19. 19.Use (a + b)(a − b) = a² − b² to find 84 × 76.
20. 20.Use (a − b)² = a² − 2ab + b² to find 95².
21. 21.Use (a + b)² = a² + 2ab + b² to find 85².
22. 22.Use a² − b² = (a + b)(a − b) to find 31² − 1².
23. 23.If a − b = 1 and ab = 72, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 53².
25. 25.Use (a + b)(a − b) = a² − b² to find 34 × 26.
26. 26.Use (a + b)(a − b) = a² − b² to find 64 × 56.
27. 27.Use a² − b² = (a + b)(a − b) to find 46² − 45².
28. 28.Find the value of x² − y² when x = 10 and y = 5.
29. 29.If a + b = 5 and ab = 6, what is a² + b²?
30. 30.If a − b = 4 and ab = 77, what is a² + b²?
31. 31.If a + b = 7 and ab = 12, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 108 × 92.
33. 33.Use (a + b)² = a² + 2ab + b² to find 11².
34. 34.Use (a − b)² = a² − 2ab + b² to find 19².
35. 35.Use (a + b)² = a² + 2ab + b² to find 33².
36. 36.If a + b = 13 and ab = 40, what is a² + b²?
37. 37.Find the value of x² − 2xy + y² when x = 12 and y = 1.
38. 38.Use a² − b² = (a + b)(a − b) to find 72² − 49².
39. 39.Use a² − b² = (a + b)(a − b) to find 41² − 35².
40. 40.If a + b = 3 and ab = 2, what is a² + b²?

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