Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 354 · 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.If a − b = 1 and ab = 2, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 49² − 2².
3. 3.Use (a + b)(a − b) = a² − b² to find 53 × 47.
4. 4.Use (a + b)(a − b) = a² − b² to find 48 × 32.
5. 5.If a − b = 2 and ab = 80, what is a² + b²?
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 3 and y = 2.
8. 8.Use a² − b² = (a + b)(a − b) to find 56² − 31².
9. 9.Use (a + b)(a − b) = a² − b² to find 65 × 55.
10. 10.Use a² − b² = (a + b)(a − b) to find 28² − 10².
11. 11.Use a² − b² = (a + b)(a − b) to find 91² − 82².
12. 12.Find the value of x² − 2xy + y² when x = 6 and y = 4.
13. 13.Use (a + b)² = a² + 2ab + b² to find 12².
14. 14.Find the value of x² − 2xy + y² when x = 12 and y = 9.
15. 15.Use (a − b)² = a² − 2ab + b² to find 93².
16. 16.Use (a + b)² = a² + 2ab + b² to find 26².
17. 17.Use (a + b)² = a² + 2ab + b² to find 52².
18. 18.Use (a − b)² = a² − 2ab + b² to find 87².
19. 19.Find the value of x² − 2xy + y² when x = 7 and y = 5.
20. 20.Find the value of x² − 2xy + y² when x = 8 and y = 2.
21. 21.If a + b = 8 and ab = 15, what is a² + b²?
22. 22.If a − b = 7 and ab = 18, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 36² − 16².
24. 24.Use (a + b)² = a² + 2ab + b² to find 54².
25. 25.If a + b = 9 and ab = 18, what is a² + b²?
26. 26.If a − b = 2 and ab = 99, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 11².
28. 28.Use a² − b² = (a + b)(a − b) to find 79² − 71².
29. 29.Use (a + b)(a − b) = a² − b² to find 66 × 54.
30. 30.Find the value of x² − 2xy + y² when x = 4 and y = 1.
31. 31.Use (a − b)² = a² − 2ab + b² to find 64².
32. 32.Use a² − b² = (a + b)(a − b) to find 85² − 34².
33. 33.Use a² − b² = (a + b)(a − b) to find 33² − 30².
34. 34.Use (a + b)² = a² + 2ab + b² to find 27².
35. 35.Use (a − b)² = a² − 2ab + b² to find 56².
36. 36.Use a² − b² = (a + b)(a − b) to find 57² − 32².
37. 37.If a + b = 14 and ab = 40, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 33².
39. 39.Use a² − b² = (a + b)(a − b) to find 67² − 6².
40. 40.Use a² − b² = (a + b)(a − b) to find 20² − 9².

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