Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 311 · 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 42 × 38.
2. 2.Use a² − b² = (a + b)(a − b) to find 42² − 39².
3. 3.Use (a + b)(a − b) = a² − b² to find 26 × 14.
4. 4.Use (a − b)² = a² − 2ab + b² to find 13².
5. 5.Find the value of x² + 2xy + y² when x = 10 and y = 6.
6. 6.Use (a + b)² = a² + 2ab + b² to find 69².
7. 7.Find the value of x² − 2xy + y² when x = 5 and y = 2.
8. 8.Use (a − b)² = a² − 2ab + b² to find 61².
9. 9.If a − b = 6 and ab = 7, what is a² + b²?
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 38² − 12².
12. 12.Use (a + b)(a − b) = a² − b² to find 31 × 29.
13. 13.Use (a − b)² = a² − 2ab + b² to find 91².
14. 14.Use (a − b)² = a² − 2ab + b² to find 96².
15. 15.Use (a + b)(a − b) = a² − b² to find 21 × 19.
16. 16.Use (a − b)² = a² − 2ab + b² to find 77².
17. 17.If a − b = 1 and ab = 12, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 24².
19. 19.Use (a + b)² = a² + 2ab + b² to find 75².
20. 20.If a − b = 3 and ab = 54, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 63².
22. 22.If a − b = 4 and ab = 5, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 23².
24. 24.Find the value of x² − 2xy + y² when x = 5 and y = 3.
25. 25.Use (a + b)(a − b) = a² − b² to find 46 × 34.
26. 26.Use a² − b² = (a + b)(a − b) to find 44² − 1².
27. 27.Use (a + b)² = a² + 2ab + b² to find 102².
28. 28.Find the value of x² − 2xy + y² when x = 9 and y = 8.
29. 29.Use (a + b)(a − b) = a² − b² to find 28 × 12.
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 1.
31. 31.Use (a − b)² = a² − 2ab + b² to find 73².
32. 32.Use (a − b)² = a² − 2ab + b² to find 87².
33. 33.Use (a − b)² = a² − 2ab + b² to find 41².
34. 34.Use (a − b)² = a² − 2ab + b² to find 71².
35. 35.Use a² − b² = (a + b)(a − b) to find 67² − 40².
36. 36.Use (a + b)² = a² + 2ab + b² to find 76².
37. 37.Use (a + b)(a − b) = a² − b² to find 38 × 22.
38. 38.Find the value of x² − y² when x = 13 and y = 1.
39. 39.If a − b = 5 and ab = 50, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 88² − 8².

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