Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 357 · 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.Find the value of x² − 2xy + y² when x = 5 and y = 4.
2. 2.Find the value of x² + 2xy + y² when x = 9 and y = 4.
3. 3.Find the value of x² + 2xy + y² when x = 9 and y = 8.
4. 4.If a + b = 10 and ab = 24, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 62 × 58.
6. 6.Find the value of x² + 2xy + y² when x = 8 and y = 7.
7. 7.Use (a + b)² = a² + 2ab + b² to find 102².
8. 8.Use a² − b² = (a + b)(a − b) to find 34² − 7².
9. 9.If a − b = 3 and ab = 88, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 82 × 78.
11. 11.Use (a − b)² = a² − 2ab + b² to find 55².
12. 12.Use (a + b)² = a² + 2ab + b² to find 22².
13. 13.Use (a + b)(a − b) = a² − b² to find 27 × 13.
14. 14.Use a² − b² = (a + b)(a − b) to find 36² − 2².
15. 15.Find the value of x² − y² when x = 6 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 26² − 12².
17. 17.Use (a + b)² = a² + 2ab + b² to find 28².
18. 18.Use (a − b)² = a² − 2ab + b² to find 18².
19. 19.Use (a + b)² = a² + 2ab + b² to find 64².
20. 20.Use a² − b² = (a + b)(a − b) to find 70² − 14².
21. 21.Use (a + b)(a − b) = a² − b² to find 108 × 92.
22. 22.Use a² − b² = (a + b)(a − b) to find 43² − 42².
23. 23.If a + b = 14 and ab = 24, what is a² + b²?
24. 24.Find the value of x² − y² when x = 3 and y = 1.
25. 25.If a + b = 8 and ab = 15, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 32².
27. 27.Use (a + b)² = a² + 2ab + b² to find 105².
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 31².
30. 30.Use a² − b² = (a + b)(a − b) to find 63² − 41².
31. 31.If a + b = 15 and ab = 54, what is a² + b²?
32. 32.If a + b = 9 and ab = 18, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 17².
34. 34.If a − b = 1 and ab = 90, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 79² − 74².
36. 36.Use a² − b² = (a + b)(a − b) to find 66² − 5².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 1.
38. 38.Use (a − b)² = a² − 2ab + b² to find 49².
39. 39.Find the value of x² − y² when x = 11 and y = 2.
40. 40.Find the value of x² + 2xy + y² when x = 4 and y = 3.

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