Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 887 · 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 53² − 32².
2. 2.Use (a + b)² = a² + 2ab + b² to find 75².
3. 3.Find the value of x² + 2xy + y² when x = 12 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 51².
5. 5.If a + b = 4 and ab = 3, what is a² + b²?
6. 6.Find the value of x² − y² when x = 11 and y = 1.
7. 7.Find the value of x² + 2xy + y² when x = 13 and y = 4.
8. 8.Use (a + b)² = a² + 2ab + b² to find 54².
9. 9.Find the value of x² − 2xy + y² when x = 14 and y = 8.
10. 10.If a + b = 9 and ab = 18, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 23² − 5².
12. 12.Find the value of x² − 2xy + y² when x = 10 and y = 4.
13. 13.Use (a + b)² = a² + 2ab + b² to find 28².
14. 14.Use (a + b)(a − b) = a² − b² to find 63 × 57.
15. 15.Use (a + b)(a − b) = a² − b² to find 24 × 16.
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.Find the value of x² − y² when x = 4 and y = 2.
18. 18.Use (a + b)(a − b) = a² − b² to find 45 × 35.
19. 19.Use a² − b² = (a + b)(a − b) to find 64² − 19².
20. 20.Use (a − b)² = a² − 2ab + b² to find 43².
21. 21.Use (a + b)² = a² + 2ab + b² to find 34².
22. 22.Use (a − b)² = a² − 2ab + b² to find 16².
23. 23.Use (a + b)² = a² + 2ab + b² to find 76².
24. 24.Use (a − b)² = a² − 2ab + b² to find 42².
25. 25.If a + b = 10 and ab = 24, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 31 × 29.
27. 27.Use (a + b)² = a² + 2ab + b² to find 21².
28. 28.If a − b = 6 and ab = 16, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 47 × 33.
30. 30.Use (a + b)(a − b) = a² − b² to find 21 × 19.
31. 31.Use (a + b)(a − b) = a² − b² to find 78 × 62.
32. 32.Use (a − b)² = a² − 2ab + b² to find 35².
33. 33.Use (a + b)² = a² + 2ab + b² to find 91².
34. 34.Use (a + b)² = a² + 2ab + b² to find 71².
35. 35.Use (a + b)² = a² + 2ab + b² to find 31².
36. 36.Use a² − b² = (a + b)(a − b) to find 61² − 20².
37. 37.Use (a + b)² = a² + 2ab + b² to find 78².
38. 38.Use (a + b)² = a² + 2ab + b² to find 81².
39. 39.Use a² − b² = (a + b)(a − b) to find 80² − 21².
40. 40.Use (a − b)² = a² − 2ab + b² to find 97².

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