Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 161 · 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 = 9 and ab = 10, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 12 and y = 11.
3. 3.Use (a − b)² = a² − 2ab + b² to find 75².
4. 4.Use (a − b)² = a² − 2ab + b² to find 96².
5. 5.Use (a − b)² = a² − 2ab + b² to find 38².
6. 6.Use (a − b)² = a² − 2ab + b² to find 43².
7. 7.If a + b = 9 and ab = 18, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 9 and y = 3.
9. 9.If a − b = 1 and ab = 2, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 18².
11. 11.Find the value of x² + 2xy + y² when x = 3 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 50² − 26².
13. 13.Use (a − b)² = a² − 2ab + b² to find 69².
14. 14.Use (a + b)² = a² + 2ab + b² to find 12².
15. 15.Use a² − b² = (a + b)(a − b) to find 31² − 13².
16. 16.Find the value of x² + 2xy + y² when x = 6 and y = 4.
17. 17.Use (a + b)(a − b) = a² − b² to find 39 × 21.
18. 18.Use (a − b)² = a² − 2ab + b² to find 13².
19. 19.Use (a + b)² = a² + 2ab + b² to find 61².
20. 20.Find the value of x² − y² when x = 10 and y = 5.
21. 21.Use (a + b)(a − b) = a² − b² to find 101 × 99.
22. 22.Find the value of x² − y² when x = 12 and y = 9.
23. 23.Use (a − b)² = a² − 2ab + b² to find 63².
24. 24.Use (a − b)² = a² − 2ab + b² to find 59².
25. 25.Use (a + b)(a − b) = a² − b² to find 58 × 42.
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.If a − b = 2 and ab = 15, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 46² − 43².
29. 29.Use (a + b)² = a² + 2ab + b² to find 68².
30. 30.Use (a + b)² = a² + 2ab + b² to find 32².
31. 31.Use (a + b)(a − b) = a² − b² to find 28 × 12.
32. 32.Use (a + b)² = a² + 2ab + b² to find 22².
33. 33.Find the value of x² − 2xy + y² when x = 8 and y = 4.
34. 34.Find the value of x² + 2xy + y² when x = 9 and y = 4.
35. 35.Find the value of x² − y² when x = 5 and y = 4.
36. 36.Find the value of x² − y² when x = 4 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 34² − 6².
38. 38.Use (a − b)² = a² − 2ab + b² to find 72².
39. 39.Use (a + b)(a − b) = a² − b² to find 105 × 95.
40. 40.Use (a − b)² = a² − 2ab + b² to find 14².

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