Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 164 · 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 − y² when x = 15 and y = 4.
2. 2.Use (a + b)² = a² + 2ab + b² to find 25².
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 3.
4. 4.Find the value of x² + 2xy + y² when x = 11 and y = 2.
5. 5.If a + b = 15 and ab = 36, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 38² − 27².
7. 7.Find the value of x² − y² when x = 4 and y = 1.
8. 8.Use (a + b)² = a² + 2ab + b² to find 78².
9. 9.Find the value of x² − 2xy + y² when x = 12 and y = 1.
10. 10.Use (a + b)² = a² + 2ab + b² to find 96².
11. 11.Use a² − b² = (a + b)(a − b) to find 54² − 18².
12. 12.Use (a − b)² = a² − 2ab + b² to find 58².
13. 13.Use (a + b)(a − b) = a² − b² to find 33 × 27.
14. 14.Use (a − b)² = a² − 2ab + b² to find 57².
15. 15.Use (a + b)(a − b) = a² − b² to find 88 × 72.
16. 16.Use (a + b)² = a² + 2ab + b² to find 106².
17. 17.Use (a + b)² = a² + 2ab + b² to find 83².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 88².
20. 20.Use (a + b)(a − b) = a² − b² to find 76 × 64.
21. 21.Use (a + b)² = a² + 2ab + b² to find 37².
22. 22.Use a² − b² = (a + b)(a − b) to find 85² − 69².
23. 23.If a + b = 6 and ab = 5, what is a² + b²?
24. 24.Find the value of x² + 2xy + y² when x = 3 and y = 2.
25. 25.Find the value of x² − y² when x = 3 and y = 2.
26. 26.Use (a + b)² = a² + 2ab + b² to find 75².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 1.
28. 28.Find the value of x² − y² when x = 12 and y = 7.
29. 29.Use (a − b)² = a² − 2ab + b² to find 65².
30. 30.Use (a + b)² = a² + 2ab + b² to find 65².
31. 31.Use (a + b)(a − b) = a² − b² to find 56 × 44.
32. 32.If a + b = 14 and ab = 24, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 16².
34. 34.Use a² − b² = (a + b)(a − b) to find 30² − 7².
35. 35.Use a² − b² = (a + b)(a − b) to find 49² − 25².
36. 36.Use a² − b² = (a + b)(a − b) to find 49² − 2².
37. 37.Use (a − b)² = a² − 2ab + b² to find 33².
38. 38.Use a² − b² = (a + b)(a − b) to find 57² − 2².
39. 39.Use (a − b)² = a² − 2ab + b² to find 69².
40. 40.If a − b = 7 and ab = 30, what is a² + b²?

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