Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 378 · 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 98².
2. 2.Use (a − b)² = a² − 2ab + b² to find 82².
3. 3.Use (a − b)² = a² − 2ab + b² to find 52².
4. 4.If a + b = 9 and ab = 18, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 77².
6. 6.Use a² − b² = (a + b)(a − b) to find 36² − 10².
7. 7.Use a² − b² = (a + b)(a − b) to find 48² − 26².
8. 8.Find the value of x² + 2xy + y² when x = 15 and y = 11.
9. 9.Use (a + b)² = a² + 2ab + b² to find 38².
10. 10.If a − b = 7 and ab = 44, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 34².
12. 12.Use (a + b)² = a² + 2ab + b² to find 49².
13. 13.Use (a + b)² = a² + 2ab + b² to find 37².
14. 14.Use (a + b)² = a² + 2ab + b² to find 61².
15. 15.Use a² − b² = (a + b)(a − b) to find 41² − 31².
16. 16.Use (a + b)(a − b) = a² − b² to find 103 × 97.
17. 17.Find the value of x² − y² when x = 6 and y = 5.
18. 18.Use (a − b)² = a² − 2ab + b² to find 22².
19. 19.Use a² − b² = (a + b)(a − b) to find 48² − 11².
20. 20.Find the value of x² + 2xy + y² when x = 6 and y = 1.
21. 21.Use (a + b)² = a² + 2ab + b² to find 73².
22. 22.Find the value of x² − y² when x = 9 and y = 4.
23. 23.Use (a + b)(a − b) = a² − b² to find 35 × 25.
24. 24.If a + b = 14 and ab = 24, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 79² − 67².
26. 26.Use a² − b² = (a + b)(a − b) to find 22² − 12².
27. 27.Use (a − b)² = a² − 2ab + b² to find 89².
28. 28.Use (a − b)² = a² − 2ab + b² to find 15².
29. 29.If a − b = 7 and ab = 8, what is a² + b²?
30. 30.If a − b = 4 and ab = 45, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 46² − 12².
32. 32.Use (a + b)² = a² + 2ab + b² to find 23².
33. 33.Use (a + b)² = a² + 2ab + b² to find 69².
34. 34.If a − b = 3 and ab = 10, what is a² + b²?
35. 35.If a − b = 2 and ab = 80, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 42 × 38.
37. 37.Use (a + b)² = a² + 2ab + b² to find 52².
38. 38.If a − b = 3 and ab = 4, what is a² + b²?
39. 39.Find the value of x² − y² when x = 8 and y = 6.
40. 40.Use (a + b)² = a² + 2ab + b² to find 39².

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