Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 252 · 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 107².
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 24 × 16.
4. 4.If a + b = 13 and ab = 30, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 16².
7. 7.If a − b = 2 and ab = 80, what is a² + b²?
8. 8.Find the value of x² − y² when x = 6 and y = 4.
9. 9.If a − b = 1 and ab = 2, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 26².
11. 11.Find the value of x² + 2xy + y² when x = 3 and y = 2.
12. 12.Use (a − b)² = a² − 2ab + b² to find 71².
13. 13.Find the value of x² − y² when x = 15 and y = 1.
14. 14.Use (a + b)(a − b) = a² − b² to find 35 × 25.
15. 15.Find the value of x² − 2xy + y² when x = 3 and y = 1.
16. 16.Find the value of x² + 2xy + y² when x = 7 and y = 1.
17. 17.If a − b = 4 and ab = 45, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 39².
19. 19.Use (a − b)² = a² − 2ab + b² to find 34².
20. 20.Use (a + b)(a − b) = a² − b² to find 36 × 24.
21. 21.Use (a + b)(a − b) = a² − b² to find 105 × 95.
22. 22.If a − b = 2 and ab = 63, what is a² + b²?
23. 23.Find the value of x² − y² when x = 12 and y = 5.
24. 24.Use (a + b)(a − b) = a² − b² to find 85 × 75.
25. 25.Find the value of x² − y² when x = 15 and y = 7.
26. 26.Use (a + b)² = a² + 2ab + b² to find 52².
27. 27.Use a² − b² = (a + b)(a − b) to find 26² − 24².
28. 28.Find the value of x² − y² when x = 4 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 23².
30. 30.Use (a + b)² = a² + 2ab + b² to find 76².
31. 31.Find the value of x² − 2xy + y² when x = 11 and y = 3.
32. 32.Use (a + b)(a − b) = a² − b² to find 61 × 59.
33. 33.Use (a + b)(a − b) = a² − b² to find 29 × 11.
34. 34.Use (a − b)² = a² − 2ab + b² to find 95².
35. 35.Use (a + b)² = a² + 2ab + b² to find 105².
36. 36.If a − b = 1 and ab = 20, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 87² − 71².
38. 38.Use (a + b)² = a² + 2ab + b² to find 103².
39. 39.Find the value of x² − 2xy + y² when x = 5 and y = 4.
40. 40.Use a² − b² = (a + b)(a − b) to find 89² − 19².

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