Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 347 · 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 67².
2. 2.Find the value of x² + 2xy + y² when x = 7 and y = 2.
3. 3.Use (a + b)² = a² + 2ab + b² to find 42².
4. 4.If a + b = 13 and ab = 30, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 54² − 47².
6. 6.Use (a − b)² = a² − 2ab + b² to find 92².
7. 7.Use (a + b)² = a² + 2ab + b² to find 93².
8. 8.Use (a + b)² = a² + 2ab + b² to find 96².
9. 9.Use (a − b)² = a² − 2ab + b² to find 55².
10. 10.Use a² − b² = (a + b)(a − b) to find 30² − 9².
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.Find the value of x² + 2xy + y² when x = 8 and y = 3.
13. 13.Use (a + b)(a − b) = a² − b² to find 77 × 63.
14. 14.Use (a + b)(a − b) = a² − b² to find 58 × 42.
15. 15.Use (a − b)² = a² − 2ab + b² to find 77².
16. 16.Find the value of x² − 2xy + y² when x = 3 and y = 2.
17. 17.Use (a − b)² = a² − 2ab + b² to find 19².
18. 18.Use (a − b)² = a² − 2ab + b² to find 65².
19. 19.Use (a − b)² = a² − 2ab + b² to find 36².
20. 20.Use (a + b)(a − b) = a² − b² to find 68 × 52.
21. 21.Use (a + b)² = a² + 2ab + b² to find 85².
22. 22.Use a² − b² = (a + b)(a − b) to find 92² − 28².
23. 23.Use (a + b)² = a² + 2ab + b² to find 15².
24. 24.Use (a + b)² = a² + 2ab + b² to find 22².
25. 25.Use a² − b² = (a + b)(a − b) to find 98² − 35².
26. 26.Find the value of x² − y² when x = 6 and y = 4.
27. 27.Use (a + b)² = a² + 2ab + b² to find 72².
28. 28.Use (a − b)² = a² − 2ab + b² to find 51².
29. 29.Use (a + b)(a − b) = a² − b² to find 105 × 95.
30. 30.Use (a + b)(a − b) = a² − b² to find 83 × 77.
31. 31.Use (a + b)(a − b) = a² − b² to find 36 × 24.
32. 32.Use (a + b)(a − b) = a² − b² to find 42 × 38.
33. 33.If a − b = 1 and ab = 20, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 47².
35. 35.Use a² − b² = (a + b)(a − b) to find 81² − 2².
36. 36.Find the value of x² − 2xy + y² when x = 3 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 43² − 2².
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 54² − 17².
40. 40.Use a² − b² = (a + b)(a − b) to find 34² − 2².

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