Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 390 · 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 a² − b² = (a + b)(a − b) to find 24² − 3².
2. 2.Use (a − b)² = a² − 2ab + b² to find 15².
3. 3.Use a² − b² = (a + b)(a − b) to find 42² − 8².
4. 4.Use (a − b)² = a² − 2ab + b² to find 38².
5. 5.Find the value of x² − 2xy + y² when x = 10 and y = 9.
6. 6.Find the value of x² − 2xy + y² when x = 8 and y = 2.
7. 7.Find the value of x² − 2xy + y² when x = 5 and y = 3.
8. 8.Use (a − b)² = a² − 2ab + b² to find 64².
9. 9.Use (a + b)² = a² + 2ab + b² to find 46².
10. 10.Use (a − b)² = a² − 2ab + b² to find 26².
11. 11.Use (a + b)² = a² + 2ab + b² to find 29².
12. 12.Use a² − b² = (a + b)(a − b) to find 55² − 20².
13. 13.If a − b = 4 and ab = 12, what is a² + b²?
14. 14.Find the value of x² + 2xy + y² when x = 9 and y = 3.
15. 15.If a − b = 2 and ab = 3, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 25².
17. 17.Find the value of x² − y² when x = 15 and y = 3.
18. 18.Use (a − b)² = a² − 2ab + b² to find 59².
19. 19.Use (a + b)² = a² + 2ab + b² to find 63².
20. 20.Use (a + b)(a − b) = a² − b² to find 97 × 83.
21. 21.Use (a + b)(a − b) = a² − b² to find 36 × 24.
22. 22.Use (a + b)² = a² + 2ab + b² to find 87².
23. 23.Use (a + b)² = a² + 2ab + b² to find 12².
24. 24.Find the value of x² − 2xy + y² when x = 10 and y = 7.
25. 25.Use (a + b)(a − b) = a² − b² to find 32 × 28.
26. 26.Use (a − b)² = a² − 2ab + b² to find 22².
27. 27.Use (a − b)² = a² − 2ab + b² to find 96².
28. 28.Use a² − b² = (a + b)(a − b) to find 81² − 12².
29. 29.Find the value of x² + 2xy + y² when x = 7 and y = 5.
30. 30.Find the value of x² − 2xy + y² when x = 8 and y = 6.
31. 31.Use (a − b)² = a² − 2ab + b² to find 89².
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.Find the value of x² − y² when x = 8 and y = 3.
34. 34.Use (a − b)² = a² − 2ab + b² to find 34².
35. 35.Use (a + b)(a − b) = a² − b² to find 57 × 43.
36. 36.Use (a − b)² = a² − 2ab + b² to find 57².
37. 37.Find the value of x² + 2xy + y² when x = 13 and y = 7.
38. 38.Find the value of x² − y² when x = 13 and y = 8.
39. 39.Use (a − b)² = a² − 2ab + b² to find 58².
40. 40.If a + b = 17 and ab = 70, what is a² + b²?

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